Diffeomorphisms in group field theories
Baratin, Aristide; Girelli, Florian; Oriti, Daniele
2011-05-15
We study the issue of diffeomorphism symmetry in group field theories (GFT), using the noncommutative metric representation introduced by A. Baratin and D. Oriti [Phys. Rev. Lett. 105, 221302 (2010).]. In the colored Boulatov model for 3d gravity, we identify a field (quantum) symmetry which ties together the vertex translation invariance of discrete gravity, the flatness constraint of canonical quantum gravity, and the topological (coarse-graining) identities for the 6j symbols. We also show how, for the GFT graphs dual to manifolds, the invariance of the Feynman amplitudes encodes the discrete residual action of diffeomorphisms in simplicial gravity path integrals. We extend the results to GFT models for higher-dimensional BF theories and discuss various insights that they provide on the GFT formalism itself.
Conformal field theory on affine Lie groups
Clubok, K.S.
1996-04-01
Working directly on affine Lie groups, we construct several new formulations of the WZW model, the gauged WZW model, and the generic affine-Virasoro action. In one formulation each of these conformal field theories (CFTs) is expressed as a one-dimensional mechanical system whose variables are coordinates on the affine Lie group. When written in terms of the affine group element, this formulation exhibits a two-dimensional WZW term. In another formulation each CFT is written as a two-dimensional field theory, with a three- dimensional WZW term, whose fields are coordinates on the affine group. On the basis of these equivalent formulations, we develop a translation dictionary in which the new formulations on the affine Lie group are understood as mode formulations of the conventional formulations on the Lie group. Using this dictionary, we also express each CFT as a three-dimensional field theory on the Lie group with a four-dimensional WZW term. 36 refs.
Recent Progress in Group Field Theory
Oriti, Daniele
2009-12-15
We introduce the key ideas behind the group field theory approach to quantum gravity, and the basic elements of its formalism. We also briefly report on some recent results obtained in this approach, concerning both the mathematical definition of these models, and possible avenues towards extracting interesting physics from them.
Double field theory on group manifolds
NASA Astrophysics Data System (ADS)
Blumenhagen, Ralph; Hassler, Falk; Lüst, Dieter
2015-02-01
A new version of double field theory (DFT) is derived for the exactly solvable background of an in general left-right asymmetric WZW model in the large level limit. This generalizes the original DFT that was derived via expanding closed string field theory on a torus up to cubic order. The action and gauge transformations are derived for fluctuations around the generalized group manifold background up to cubic order, revealing the appearance of a generalized Lie derivative and a corresponding C-bracket upon invoking a new version of the strong constraint. In all these quantities a background dependent covariant derivative appears reducing to the partial derivative for a toroidal background. This approach sheds some new light on the conceptual status of DFT, its background (in-)dependence and the up-lift of non-geometric Scherk-Schwarz reductions.
Working Group Report: Lattice Field Theory
Blum, T.; et al.,
2013-10-22
This is the report of the Computing Frontier working group on Lattice Field Theory prepared for the proceedings of the 2013 Community Summer Study ("Snowmass"). We present the future computing needs and plans of the U.S. lattice gauge theory community and argue that continued support of the U.S. (and worldwide) lattice-QCD effort is essential to fully capitalize on the enormous investment in the high-energy physics experimental program. We first summarize the dramatic progress of numerical lattice-QCD simulations in the past decade, with some emphasis on calculations carried out under the auspices of the U.S. Lattice-QCD Collaboration, and describe a broad program of lattice-QCD calculations that will be relevant for future experiments at the intensity and energy frontiers. We then present details of the computational hardware and software resources needed to undertake these calculations.
Gauge field theory for the Poincaré-Weyl group
NASA Astrophysics Data System (ADS)
Babourova, O. V.; Frolov, B. N.; Zhukovsky, V. Ch.
2006-09-01
On the basis of the general principles of a gauge field theory, the gauge theory for the Poincaŕe-Weyl group is constructed. It is shown that tetrads are not true gauge fields, but represent functions of true gauge fields: Lorentzian, translational, and dilatational ones. The equations for gauge fields are obtained. Geometrical interpretation of the theory is developed demonstrating that as a result of localization of the Poincaré-Weyl group the space-time becomes a Weyl-Cartan space. The geometrical interpretation of a dilaton field as a component of the metric tensor of a tangent space in Weyl-Cartan geometry is also proposed.
Group field theories for all loop quantum gravity
NASA Astrophysics Data System (ADS)
Oriti, Daniele; Ryan, James P.; Thürigen, Johannes
2015-02-01
Group field theories represent a second quantized reformulation of the loop quantum gravity state space and a completion of the spin foam formalism. States of the canonical theory, in the traditional continuum setting, have support on graphs of arbitrary valence. On the other hand, group field theories have usually been defined in a simplicial context, thus dealing with a restricted set of graphs. In this paper, we generalize the combinatorics of group field theories to cover all the loop quantum gravity state space. As an explicit example, we describe the group field theory formulation of the KKL spin foam model, as well as a particular modified version. We show that the use of tensor model tools allows for the most effective construction. In order to clarify the mathematical basis of our construction and of the formalisms with which we deal, we also give an exhaustive description of the combinatorial structures entering spin foam models and group field theories, both at the level of the boundary states and of the quantum amplitudes.
Cosmology from group field theory formalism for quantum gravity.
Gielen, Steffen; Oriti, Daniele; Sindoni, Lorenzo
2013-07-19
We identify a class of condensate states in the group field theory (GFT) formulation of quantum gravity that can be interpreted as macroscopic homogeneous spatial geometries. We then extract the dynamics of such condensate states directly from the fundamental quantum GFT dynamics, following the procedure used in ordinary quantum fluids. The effective dynamics is a nonlinear and nonlocal extension of quantum cosmology. We also show that any GFT model with a kinetic term of Laplacian type gives rise, in a semiclassical (WKB) approximation and in the isotropic case, to a modified Friedmann equation. This is the first concrete, general procedure for extracting an effective cosmological dynamics directly from a fundamental theory of quantum geometry.
Functional renormalization group analysis of tensorial group field theories on Rd
NASA Astrophysics Data System (ADS)
Geloun, Joseph Ben; Martini, Riccardo; Oriti, Daniele
2016-07-01
Rank-d tensorial group field theories are quantum field theories (QFTs) defined on a group manifold G×d , which represent a nonlocal generalization of standard QFT and a candidate formalism for quantum gravity, since, when endowed with appropriate data, they can be interpreted as defining a field theoretic description of the fundamental building blocks of quantum spacetime. Their renormalization analysis is crucial both for establishing their consistency as quantum field theories and for studying the emergence of continuum spacetime and geometry from them. In this paper, we study the renormalization group flow of two simple classes of tensorial group field theories (TGFTs), defined for the group G =R for arbitrary rank, both without and with gauge invariance conditions, by means of functional renormalization group techniques. The issue of IR divergences is tackled by the definition of a proper thermodynamic limit for TGFTs. We map the phase diagram of such models, in a simple truncation, and identify both UV and IR fixed points of the RG flow. Encouragingly, for all the models we study, we find evidence for the existence of a phase transition of condensation type.
Flat connection, conformal field theory and quantum group
Kato, Mitsuhiro.
1989-07-01
General framework of linear first order differential equation for four-point conformal block is studied by using flat connection. Integrability and SL{sub 2} invariance restrict possible form of flat connection. Under a special ansatz classical Yang-Baxter equation appears as an integrability condition and the WZW model turns to be unique conformal field theory in that case. Monodromy property of conformal block can be easily determined by the flat connection. 11 refs.
Gravity as an internal Yang-Mills gauge field theory of the Poincaré group.
NASA Astrophysics Data System (ADS)
Hennig, Jörg; Nitsch, Jürgen
1981-10-01
In the framework of affine bundles we present gravity as an “internal” gauge field theory of the Poincaré group. The resulting geometry is a Riemann-Cartan space-time carrying torsion and curvature. In order to admit a nontrivial action of the translation group we formally extend the matter Lagrangian to affine field variables. Finally, we establish the relation of our approach with the formalism of Hehl et al.
Crystal Field Theory and the Angular Overlap Model Applied to Hydrides of Main Group Elements.
ERIC Educational Resources Information Center
Moore, E. A.
1990-01-01
Described is how crystal field theory and the angular overlap model can be applied to very simple molecules which can then be used to introduce such concepts as bonding orbitals, MO diagrams, and Walsh diagrams. The main-group compounds are used as examples and a switch to the transition metal complexes. (KR)
NASA Astrophysics Data System (ADS)
de Cesare, Marco; Pithis, Andreas G. A.; Sakellariadou, Mairi
2016-09-01
We study the cosmological implications of interactions between spacetime quanta in the group field theory (GFT) approach to quantum gravity from a phenomenological perspective. Our work represents a first step towards understanding early Universe cosmology by studying the dynamics of the emergent continuum spacetime, as obtained from a fundamentally discrete microscopic theory. In particular, we show how GFT interactions lead to a recollapse of the Universe while preserving the bounce replacing the initial singularity, which has already been shown to occur in the free case. It is remarkable that cyclic cosmologies are thus obtained in this framework without any a priori assumption on the geometry of spatial sections of the emergent spacetime. Furthermore, we show how interactions make it possible to have an early epoch of accelerated expansion, which can be made to last for an arbitrarily large number of e -folds, without the need to introduce an ad hoc potential for the scalar field.
Group field theory as the second quantization of loop quantum gravity
NASA Astrophysics Data System (ADS)
Oriti, Daniele
2016-04-01
We construct a second quantized reformulation of canonical loop quantum gravity (LQG) at both kinematical and dynamical level, in terms of a Fock space of spin networks, and show in full generality that it leads directly to the group field theory (GFT) formalism. In particular, we show the correspondence between canonical LQG dynamics and GFT dynamics leading to a specific GFT model from any definition of quantum canonical dynamics of spin networks. We exemplify the correspondence of dynamics in the specific example of 3d quantum gravity. The correspondence between canonical LQG and covariant spin foam models is obtained via the GFT definition of the latter.
Renormalization-group theory for the phase-field crystal equation
NASA Astrophysics Data System (ADS)
Athreya, Badrinarayan P.; Goldenfeld, Nigel; Dantzig, Jonathan A.
2006-07-01
We derive a set of rotationally covariant amplitude equations for use in multiscale simulation of the two-dimensional phase-field crystal model by a variety of renormalization-group (RG) methods. We show that the presence of a conservation law introduces an ambiguity in operator ordering in the RG procedure, which we show how to resolve. We compare our analysis with standard multiple-scale techniques, where identical results can be obtained with greater labor, by going to sixth order in perturbation theory, and by assuming the correct scaling of space and time.
Impact of nonlinear effective interactions on group field theory quantum gravity condensates
NASA Astrophysics Data System (ADS)
Pithis, Andreas G. A.; Sakellariadou, Mairi; Tomov, Petar
2016-09-01
We present the numerical analysis of effectively interacting group field theory models in the context of the group field theory quantum gravity condensate analog of the Gross-Pitaevskii equation for real Bose-Einstein condensates including combinatorially local interaction terms. Thus, we go beyond the usually considered construction for free models. More precisely, considering such interactions in a weak regime, we find solutions for which the expectation value of the number operator N is finite, as in the free case. When tuning the interaction to the strongly nonlinear regime, however, we obtain solutions for which N grows and eventually blows up, which is reminiscent of what one observes for real Bose-Einstein condensates, where a strong interaction regime can only be realized at high density. This behavior suggests the breakdown of the Bogoliubov ansatz for quantum gravity condensates and the need for non-Fock representations to describe the system when the condensate constituents are strongly correlated. Furthermore, we study the expectation values of certain geometric operators imported from loop quantum gravity in the free and interacting cases. In particular, computing solutions around the nontrivial minima of the interaction potentials, one finds, already in the weakly interacting case, a nonvanishing condensate population for which the spectra are dominated by the lowest nontrivial configuration of the quantum geometry. This result indicates that the condensate may indeed consist of many smallest building blocks giving rise to an effectively continuous geometry, thus suggesting the interpretation of the condensate phase to correspond to a geometric phase.
NASA Astrophysics Data System (ADS)
Harada, Koji; Sasabe, Satoru; Yahiro, Masanobu
2016-08-01
We formulate the next-to-leading-order nuclear effective field theory without pions in the two-nucleon sector on a spatial lattice and investigate nonperturbative renormalization group flows in the strong-coupling region by diagonalizing the Hamiltonian numerically. The cutoff (proportional to the inverse of the lattice constant) dependence of the coupling constants is obtained by changing the lattice constant with the binding energy and the asymptotic normalization constant for the ground state being fixed. We argue that the critical line can be obtained by looking at the finite-size dependence of the ground-state energy. We determine the relevant operator and locate the nontrivial fixed point, as well as the physical flow line corresponding to the deuteron in the two-dimensional plane of dimensionless coupling constants. It turns out that the location of the nontrivial fixed point is very close to the one obtained by the corresponding analytic calculation, but the relevant operator is quite different.
Emergence of a low spin phase in group field theory condensates
NASA Astrophysics Data System (ADS)
Gielen, Steffen
2016-11-01
Recent results have shown how quantum cosmology models can be derived from the effective dynamics of condensate states in group field theory (GFT), where ‘cosmology is the hydrodynamics of quantum gravity’: the classical Friedmann dynamics for homogeneous, isotropic universes, as well as loop quantum cosmology (LQC) corrections to general relativity have been shown to emerge from fundamental quantum gravity. We take one further step towards strengthening the link with LQC and show, in a class of GFT models for gravity coupled to a free massless scalar field and for generic initial conditions, that GFT condensates dynamically reach a low spin phase of many quanta of geometry, in which all but an exponentially small number of quanta are characterised by a single spin j 0 (i.e. by a constant volume per quantum). As the low spin regime is reached, GFT condensates expand to exponentially large volumes, and the dynamics of the total volume follows precisely the classical Friedmann equations. This behaviour follows from a single requirement on the couplings in the GFT model under study. We present one particular simple case in which the dominant spin is the lowest one: {j}0=0 or, if this is excluded, {j}0=1/2. The type of quantum state usually assumed in the derivation of LQC is hence derived from the quantum dynamics of GFT. These results confirm and extend recent results by Oriti, Sindoni and Wilson-Ewing in the same setting.
NASA Astrophysics Data System (ADS)
Dankova, T. S.; Rosensteel, G.
1998-10-01
Mean field theory has an unexpected group theoretic mathematical foundation. Instead of representation theory which applies to most group theoretic quantum models, Hartree-Fock and Hartree-Fock-Bogoliubov have been formulated in terms of coadjoint orbits for the groups U(n) and O(2n). The general theory of mean fields is formulated for an arbitrary Lie algebra L of fermion operators. The moment map provides the correspondence between the Hilbert space of microscopic wave functions and the dual space L^* of densities. The coadjoint orbits of the group in the dual space are phase spaces on which time-dependent mean field theory is equivalent to a classical Hamiltonian dynamical system. Indeed it forms a finite-dimensional Lax system. The mean field theories for the Elliott SU(3) and symplectic Sp(3,R) algebras are constructed explicitly in the coadjoint orbit framework.
Derivative expansions of renormaliztion group effective potentials for {phi}{sup 4} field theories
Shepard, J.R.; McNeil, J.A.
1995-10-01
We approximate an exact Renormalization Group (RG) equation for the flow of the effective action of {phi}{sup 4} field theories by including next-to-leading order (NLO) terms in a derivative expansion. This level of approximation allows us to treat effects of wavefunction renormalization which are beyond the scope of the leading order (LO) formulation. We compare calculations based on a {open_quote}latticized {close_quotes} version of our RG equation in 3 Euclidean dimensions directly with Monte Carlo (MC) results and find excellent overall agreement as well as substantial improvement over LO calculations. We solve the continuum form of our equation to find the Wilson fixed point and determine the critical exponent {eta} (0.046). We also find the critical exponents {nu} (0.666) and {omega} (0.735). These latter two are in much improved agreement with {open_quote}world`s best{close_quotes} values com- pared to those obtained at LO (where no prediction for {eta} is possible). We also find that the {open_quote}universal potential{close_quote} determined via MC methods by Tsypin can be understood quantitatively using our NLO RG equations. Careful analysis shows that ambiguities which plague {open_quote}smooth cutoff{close_quotes} formulations do not arise with our RG equations.
Renormalization of the periodic scalar field theory by Polchinski's renormalization group method
NASA Astrophysics Data System (ADS)
Nándori, I.; Sailer, K.; Jentschura, U. D.; Soff, G.
2002-04-01
The renormalization group (RG) flow for the two-dimensional sine-Gordon model is determined by means of Polchinski's RG equation at next-to-leading order in the derivative expansion. In this paper, we have two different goals, (i) to consider the renormalization scheme-dependence of Polchinski's method by matching Polchinski's equation with the Wegner-Houghton equation and with the real space RG equations for the two-dimensional dilute Coulomb-gas, (ii) to go beyond the local potential approximation in the gradient expansion in order to clarify the supposed role of the field-dependent wave-function renormalization. The well-known Coleman fixed point of the sine-Gordon model is recovered after linearization, whereas the flow exhibits strong dependence on the choice of the renormalization scheme when non-linear terms are kept. The RG flow is compared to those obtained in the Wegner-Houghton approach and in the dilute gas approximation for the two-dimensional Coulomb-gas.
Gauge groups and matter fields on some models of F-theory without section
NASA Astrophysics Data System (ADS)
Kimura, Yusuke
2016-03-01
We investigate F-theory on an elliptic Calabi-Yau 4-fold without a section to the fibration. To construct an elliptic Calabi-Yau 4-fold without a section, we introduce families of elliptic K3 surfaces which do not admit a section. A product K3 × K3, with one of the K3's chosen from these families of elliptic K3 surfaces without a section, realises an elliptic Calabi-Yau 4-fold without a section. We then compactify F-theory on such K3 × K3's.
NASA Astrophysics Data System (ADS)
Wang, Juven; Gu, Zheng-Cheng; Wen, Xiao-Gang
The challenge of identifying symmetry-protected topological states (SPTs) is due to their lack of symmetry-breaking order parameters and intrinsic topological orders. For this reason, it is impossible to formulate SPTs under Ginzburg-Landau theory or probe SPTs via fractionalized bulk excitations and topology-dependent ground state degeneracy. However, the partition functions from path integrals with various symmetry twists are universal SPT invariants, fully characterizing SPTs. In this work, we use gauge fields to represent those symmetry twists in closed spacetimes of any dimensionality and arbitrary topology. This allows us to express the SPT invariants in terms of continuum field theory. We show that SPT invariants of pure gauge actions describe the SPTs predicted by group cohomology, while the mixed gauge-gravity actions describe the beyond-group-cohomology SPTs, recently observed by Kapustin. We find new examples of mixed gauge-gravity actions for U(1) SPTs in 3+1D and 4+1D via the Stiefel-Whitney class and the gravitational Chern-Simons term. [Work based on Phys. Rev. Lett. 114, 031601 (2015) arXiv:1405.7689
NASA Technical Reports Server (NTRS)
Holman, Gordon D.
1989-01-01
The primary purpose of the Theory and Modeling Group meeting was to identify scientists engaged or interested in theoretical work pertinent to the Max '91 program, and to encourage theorists to pursue modeling which is directly relevant to data which can be expected to result from the program. A list of participants and their institutions is presented. Two solar flare paradigms were discussed during the meeting -- the importance of magnetic reconnection in flares and the applicability of numerical simulation results to solar flare studies.
Kheirandish, F.; Amooshahi, M.
2008-11-18
Quantum field theory of a damped vibrating string as the simplest dissipative scalar field theory is investigated by introducing a minimal coupling method. The rate of energy flowing between the system and its environment is obtained.
Covariant Noncommutative Field Theory
Estrada-Jimenez, S.; Garcia-Compean, H.; Obregon, O.; Ramirez, C.
2008-07-02
The covariant approach to noncommutative field and gauge theories is revisited. In the process the formalism is applied to field theories invariant under diffeomorphisms. Local differentiable forms are defined in this context. The lagrangian and hamiltonian formalism is consistently introduced.
ERIC Educational Resources Information Center
Morpurgo, Simone
2007-01-01
The principles of symmetry and group theory are applied to the zero-order wavefunctions associated with the strong-field t[subscript 2g][superscript 2] configuration and their symmetry-adapted linear combinations (SALC) associated with the generated energy terms are derived. This approach will enable students to better understand the use of…
Introduction to Statistical Field Theory
NASA Astrophysics Data System (ADS)
Brézin, Edouard
2010-07-01
1. A few well-known basic results; 2. Introduction: order parameters, broken symmetries; 3. Examples of physical situations modelled by the Ising model; 4. A few results about the Ising model; 5. High temperature and low temperature expansions; 6. Some geometric problems related to phase transitions; 7. Phenomenological description of the critical behaviour; 8. Mean field theory; 9. Beyond mean field theory; 10. Introduction to the renormalization group; 11. Renormalization group for the φ4 theory; 12. Renormalized theory; 13. Goldstone modes; 14. Large n; Index.
NASA Astrophysics Data System (ADS)
Kwak, Seung Ki
The existence of momentum and winding modes of closed string on a torus leads to a natural idea that the field theoretical approach of string theory should involve winding type coordinates as well as the usual space-time coordinates. Recently developed double field theory is motivated from this idea and it implements T-duality manifestly by doubling the coordinates. In this thesis we will mainly focus on the double field theory formulation of different string theories in its low energy limit: bosonic, heterotic, type II and its massive extensions, and N = 1 supergravity theory. In chapter 2 of the thesis we study the equivalence of different formulations of double field theory. There are three different formulations of double field theory: background field E formulation, generalized metric H formulation, and frame field EAM formulation. Starting from the frame field formalism and choosing an appropriate gauge, the equivalence of the three formulations of bosonic theory are explicitly verified. In chapter 3 we construct the double field theory formulation of heterotic strings. The global symmetry enlarges to O( D, D + n) for heterotic strings and the enlarged generalized metric features this symmetry. The structural form of bosonic theory can directly be applied to the heterotic theory with the enlarged generalized metric. In chapter 4 we develop a unified framework of double field theory for type II theories. The Ramond-Ramond potentials fit into spinor representations of the duality group O( D, D) and the theory displays Spin+( D, D) symmetry with its self-duality relation. For a specific form of RR 1-form the theory reduces to the massive deformation of type IIA theory due to Romans. In chapter 5 we formulate the N = 1 supersymmetric extension of double field theory including the coupling to n abelian vector multiplets. This theory features a local O(1, 9 + n) x O(1, 9) tangent space symmetry under which the fermions transform. (Copies available exclusively from
Naive Theories of Social Groups
ERIC Educational Resources Information Center
Rhodes, Marjorie
2012-01-01
Four studies examined children's (ages 3-10, Total N = 235) naive theories of social groups, in particular, their expectations about how group memberships constrain social interactions. After introduction to novel groups of people, preschoolers (ages 3-5) reliably expected agents from one group to harm members of the other group (rather than…
Logarithmic conformal field theory
NASA Astrophysics Data System (ADS)
Gainutdinov, Azat; Ridout, David; Runkel, Ingo
2013-12-01
Conformal field theory (CFT) has proven to be one of the richest and deepest subjects of modern theoretical and mathematical physics research, especially as regards statistical mechanics and string theory. It has also stimulated an enormous amount of activity in mathematics, shaping and building bridges between seemingly disparate fields through the study of vertex operator algebras, a (partial) axiomatisation of a chiral CFT. One can add to this that the successes of CFT, particularly when applied to statistical lattice models, have also served as an inspiration for mathematicians to develop entirely new fields: the Schramm-Loewner evolution and Smirnov's discrete complex analysis being notable examples. When the energy operator fails to be diagonalisable on the quantum state space, the CFT is said to be logarithmic. Consequently, a logarithmic CFT is one whose quantum space of states is constructed from a collection of representations which includes reducible but indecomposable ones. This qualifier arises because of the consequence that certain correlation functions will possess logarithmic singularities, something that contrasts with the familiar case of power law singularities. While such logarithmic singularities and reducible representations were noted by Rozansky and Saleur in their study of the U (1|1) Wess-Zumino-Witten model in 1992, the link between the non-diagonalisability of the energy operator and logarithmic singularities in correlators is usually ascribed to Gurarie's 1993 article (his paper also contains the first usage of the term 'logarithmic conformal field theory'). The class of CFTs that were under control at this time was quite small. In particular, an enormous amount of work from the statistical mechanics and string theory communities had produced a fairly detailed understanding of the (so-called) rational CFTs. However, physicists from both camps were well aware that applications from many diverse fields required significantly more
ERIC Educational Resources Information Center
Huetinck, Linda
1996-01-01
Introduces concepts of modern algebraic group theory in the form of a game. Peg boards and rubber bands represent nonnumerical group elements and are manipulated under the operation of reorienting a regular polygon. Symmetry groups are used to explore set properties, as well as commutative and noncommutative operations. (CMS)
Remainder Wheels and Group Theory
ERIC Educational Resources Information Center
Brenton, Lawrence
2008-01-01
Why should prospective elementary and high school teachers study group theory in college? This paper examines applications of abstract algebra to the familiar algorithm for converting fractions to repeating decimals, revealing ideas of surprising substance beneath an innocent facade.
NASA Astrophysics Data System (ADS)
You, Setthivoine
2015-11-01
A new canonical field theory has been developed to help interpret the interaction between plasma flows and magnetic fields. The theory augments the Lagrangian of general dynamical systems to rigourously demonstrate that canonical helicity transport is valid across single particle, kinetic and fluid regimes, on scales ranging from classical to general relativistic. The Lagrangian is augmented with two extra terms that represent the interaction between the motion of matter and electromagnetic fields. The dynamical equations can then be re-formulated as a canonical form of Maxwell's equations or a canonical form of Ohm's law valid across all non-quantum regimes. The field theory rigourously shows that helicity can be preserved in kinetic regimes and not only fluid regimes, that helicity transfer between species governs the formation of flows or magnetic fields, and that helicity changes little compared to total energy only if density gradients are shallow. The theory suggests a possible interpretation of particle energization partitioning during magnetic reconnection as canonical wave interactions. This work is supported by US DOE Grant DE-SC0010340.
Geometer energy unified field theory
NASA Astrophysics Data System (ADS)
Rivera, Susana; Rivera, Anacleto
GEOMETER - ENERGY UNIFIED FIELD THEORY Author: Anacleto Rivera Nivón Co-author: Susana Rivera Cabrera This work is an attempt to find the relationship between the Electromagnetic Field and the Gravitational Field. Despite it is based on the existence of Strings of Energy, it is not the same kind of strings that appears on other theories like Superstring Theory, Branas Theory, M - Theory, or any other related string theories. Here, the Strings are concentrated energy lines that vibrates, and experiences shrinking and elongations, absorbing and yielding on each contraction and expansion all that is found in the Universe: matter and antimatter, waves and energy in all manifestations. In contrast to superstring theory, which strings are on the range of the Length of Planck, these Strings can be on the cosmological size, and can contain many galaxies, or clusters, or groups of galaxies; but also they can reach as small sizes as subatomic levels. Besides, and contrary to what it is stated in some other string theories that need the existence of ten or more dimensions, the present proposal sustains in only four particular dimensions. It has been developed a mathematical support that will try to help to improve the understanding of the phenomena that take place at the Universe.
Extended conformal field theories
NASA Astrophysics Data System (ADS)
Taormina, Anne
1990-08-01
Some extended conformal field theories are briefly reviewed. They illustrate how non minimal models of the Virasoro algebra (c≥1) can become minimal with respect to a larger algebra. The accent is put on N-extended superconformal algebras, which are relevant in superstring compactification.
Holographic effective field theories
NASA Astrophysics Data System (ADS)
Martucci, Luca; Zaffaroni, Alberto
2016-06-01
We derive the four-dimensional low-energy effective field theory governing the moduli space of strongly coupled superconformal quiver gauge theories associated with D3-branes at Calabi-Yau conical singularities in the holographic regime of validity. We use the dual supergravity description provided by warped resolved conical geometries with mobile D3-branes. Information on the baryonic directions of the moduli space is also obtained by using wrapped Euclidean D3-branes. We illustrate our general results by discussing in detail their application to the Klebanov-Witten model.
Beyond mean field theory: statistical field theory for neural networks
Buice, Michael A; Chow, Carson C
2014-01-01
Mean field theories have been a stalwart for studying the dynamics of networks of coupled neurons. They are convenient because they are relatively simple and possible to analyze. However, classical mean field theory neglects the effects of fluctuations and correlations due to single neuron effects. Here, we consider various possible approaches for going beyond mean field theory and incorporating correlation effects. Statistical field theory methods, in particular the Doi–Peliti–Janssen formalism, are particularly useful in this regard. PMID:25243014
Logarithmic conformal field theory
NASA Astrophysics Data System (ADS)
Gainutdinov, Azat; Ridout, David; Runkel, Ingo
2013-12-01
Conformal field theory (CFT) has proven to be one of the richest and deepest subjects of modern theoretical and mathematical physics research, especially as regards statistical mechanics and string theory. It has also stimulated an enormous amount of activity in mathematics, shaping and building bridges between seemingly disparate fields through the study of vertex operator algebras, a (partial) axiomatisation of a chiral CFT. One can add to this that the successes of CFT, particularly when applied to statistical lattice models, have also served as an inspiration for mathematicians to develop entirely new fields: the Schramm-Loewner evolution and Smirnov's discrete complex analysis being notable examples. When the energy operator fails to be diagonalisable on the quantum state space, the CFT is said to be logarithmic. Consequently, a logarithmic CFT is one whose quantum space of states is constructed from a collection of representations which includes reducible but indecomposable ones. This qualifier arises because of the consequence that certain correlation functions will possess logarithmic singularities, something that contrasts with the familiar case of power law singularities. While such logarithmic singularities and reducible representations were noted by Rozansky and Saleur in their study of the U (1|1) Wess-Zumino-Witten model in 1992, the link between the non-diagonalisability of the energy operator and logarithmic singularities in correlators is usually ascribed to Gurarie's 1993 article (his paper also contains the first usage of the term 'logarithmic conformal field theory'). The class of CFTs that were under control at this time was quite small. In particular, an enormous amount of work from the statistical mechanics and string theory communities had produced a fairly detailed understanding of the (so-called) rational CFTs. However, physicists from both camps were well aware that applications from many diverse fields required significantly more
NASA Astrophysics Data System (ADS)
Ginzburg, V. B.
1996-09-01
A toroidal spiral field is introduced that propagates around all the objects in the universe. The nature of this field can be either gravitational or electrostatic or magnetic, and it governs the motion of the objects as well as the forces that act upon them. The topology of the toroidal spiral field is obtained when the Bertrami vortex comprised of two helical fluxes of opposite vorticity is curved into a circle. The main parameter that defines the geometry of the toroidal spiral field is the inversion radius of a sphere at which the toroidal fluxes of opposite vorticity meet. The inversion sphere is the border surface at which the matter converts into anti-matter, and at which the law of physics are inverted. The theory covers the problem of two objects orbiting each other with possible sizes ranging from an elementary particle to a black hole and to a galaxy. The equations obtained define the radii of the stationary quantum orbits which can be applied to a structure of the hydrogen atom, including its nucleus, as well as to a structure of a planetary system and a black hole. They also establish the relativistic relationships for the gravitational and inertial masses as well as for the electrical charge which are quite different than those proposed by Lorentz.
Groups in the radiative transfer theory
NASA Astrophysics Data System (ADS)
Nikoghossian, Arthur
2016-11-01
The paper presents a group-theoretical description of radiation transfer in inhomogeneous and multi-component atmospheres with the plane-parallel geometry. It summarizes and generalizes the results obtained recently by the author for some standard transfer problems of astrophysical interest with allowance of the angle and frequency distributions of the radiation field. We introduce the concept of composition groups for media with different optical and physical properties. Group representations are derived for two possible cases of illumination of a composite finite atmosphere. An algorithm for determining the reflectance and transmittance of inhomogeneous and multi-component atmospheres is described. The group theory is applied also to determining the field of radiation inside an inhomogeneous atmosphere. The concept of a group of optical depth translations is introduced. The developed theory is illustrated with the problem of radiation diffusion with partial frequency distribution assuming that the inhomogeneity is due to depth-variation of the scattering coefficient. It is shown that once reflectance and transmittance of a medium are determined, the internal field of radiation in the source-free atmosphere is found without solving any new equations. The transfer problems for a semi-infinite atmosphere and an atmosphere with internal sources of energy are discussed. The developed theory allows to derive summation laws for the mean number of scattering events underwent by the photons in the course of diffusion in the atmosphere.
Field theory of pattern identification
NASA Astrophysics Data System (ADS)
Agu, Masahiro
1988-06-01
Based on the psychological experimental fact that images in mental space are transformed into other images for pattern identification, a field theory of pattern identification of geometrical patterns is developed with the use of gauge field theory in Euclidean space. Here, the ``image'' or state function ψ[χ] of the brain reacting to a geometrical pattern χ is made to correspond to the electron's wave function in Minkowski space. The pattern identification of the pattern χ with the modified pattern χ+Δχ is assumed to be such that their images ψ[χ] and ψ[χ+Δχ] in the brain are transformable with each other through suitable transformation groups such as parallel transformation, dilatation, or rotation. The transformation group is called the ``image potential'' which corresponds to the vector potential of the gauge field. An ``image field'' derived from the image potential is found to be induced in the brain when the two images ψ[χ] and ψ[χ+Δχ] are not transformable through suitable transformation groups or gauge transformations. It is also shown that, when the image field exists, the final state of the image ψ[χ] is expected to be different, depending on the paths of modifications of the pattern χ leading to a final pattern. The above fact is interpreted as a version of the Aharonov and Bohm effect of the electron's wave function [A. Aharonov and D. Bohm, Phys. Rev. 115, 485 (1959)]. An excitation equation of the image field is also derived by postulating that patterns are identified maximally for the purpose of minimizing the number of memorized standard patterns.
Katanin, A. A.
2015-06-15
We consider formulations of the functional renormalization-group (fRG) flow for correlated electronic systems with the dynamical mean-field theory as a starting point. We classify the corresponding renormalization-group schemes into those neglecting one-particle irreducible six-point vertices (with respect to the local Green’s functions) and neglecting one-particle reducible six-point vertices. The former class is represented by the recently introduced DMF{sup 2}RG approach [31], but also by the scale-dependent generalization of the one-particle irreducible representation (with respect to local Green’s functions, 1PI-LGF) of the generating functional [20]. The second class is represented by the fRG flow within the dual fermion approach [16, 32]. We compare formulations of the fRG approach in each of these cases and suggest their further application to study 2D systems within the Hubbard model.
Quantum field theory of fluids.
Gripaios, Ben; Sutherland, Dave
2015-02-20
The quantum theory of fields is largely based on studying perturbations around noninteracting, or free, field theories, which correspond to a collection of quantum-mechanical harmonic oscillators. The quantum theory of an ordinary fluid is "freer", in the sense that the noninteracting theory also contains an infinite collection of quantum-mechanical free particles, corresponding to vortex modes. By computing a variety of correlation functions at tree and loop level, we give evidence that a quantum perfect fluid can be consistently formulated as a low-energy, effective field theory. We speculate that the quantum behavior is radically different from both classical fluids and quantum fields.
Gauge theory of Virasoro-Kac-Moody group
NASA Astrophysics Data System (ADS)
Cho, Y. M.; Zoh, S. W.
1992-10-01
We present a prototype gauge theory of the Virasoro-Kac-Moody symmetry associated with an arbitrary grand unified group G, which could be interpreted as an effective field theory of a colored string. The theory automatically breaks the symmetry down to H⊗U(1), where H is a subgroup of G and U(1) is the Cartan subgroup of the Virasoro group. After the inevitable spontaneous symmetry breaking the particle spectrum of the theory consists of an infinite tower of massive spin-one fields, the massless gauge fields of the unbroken subgroup, and the light scalar fields which become the pseudo-Goldstone fields of the symmetry breaking
Dyons in topological field theories
NASA Astrophysics Data System (ADS)
Temple-Raston, M.
1991-10-01
We examine a class of topological field theories defined by Lagrangians that under certain conditions can be written as the sum of two characteristic numbers or winding numbers. Therefore, the action or the energy is a topological invariant and stable under perturbations. The sufficient conditions required for stability take the form of first-order field equations, analogous to the self-duality and Bogomol'nyi equations in Yang-Mills(-Higgs) theory. Solutions to the first-order equations automatically satisfy the full field equations. We show the existence of nontrivial, nonsingular, minimum energy spherically symmetric dyon solutions and that they are stable. We also discuss evidence for a dual field theory to Yang-Mills-Higgs in topological field theory. The existence of dual field theories and electric monopoles is predicted by Montonen and Olive.
Extending Sociocultural Theory to Group Creativity
ERIC Educational Resources Information Center
Sawyer, Keith
2012-01-01
Sociocultural theory focuses on group processes through time, and argues that group phenomena cannot be reduced to explanation in terms of the mental states or actions of the participating individuals. This makes sociocultural theory particularly useful in the analysis of group creativity and group learning, because both group creativity and group…
Attachment Theory: Contributions to Group Work.
ERIC Educational Resources Information Center
Pistole, M. Carole
1997-01-01
Describes attachment theory, explores its application to group counseling, and elaborates points of interest to group workers. Focuses on attachment styles, attachment and caregiving, the group leader's goals, the group as an attachment experience, interventions based on attachment theory, its use in psychoeducational groups, and complexities in…
Invariants from classical field theory
Diaz, Rafael; Leal, Lorenzo
2008-06-15
We introduce a method that generates invariant functions from perturbative classical field theories depending on external parameters. By applying our methods to several field theories such as Abelian BF, Chern-Simons, and two-dimensional Yang-Mills theory, we obtain, respectively, the linking number for embedded submanifolds in compact varieties, the Gauss' and the second Milnor's invariant for links in S{sup 3}, and invariants under area-preserving diffeomorphisms for configurations of immersed planar curves.
The Nonlinear Field Space Theory
NASA Astrophysics Data System (ADS)
Mielczarek, Jakub; Trześniewski, Tomasz
2016-08-01
In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space may have nontrivial geometry has attracted significant attention, especially in the context of quantum gravity. The aim of this letter is to extend this concept to the domain of field theories, by introducing field spaces (i.e. phase spaces of field values) that are not affine spaces. After discussing the motivation and general aspects of our approach we present a detailed analysis of the prototype (quantum) Nonlinear Field Space Theory of a scalar field on the Minkowski background. We show that the nonlinear structure of a field space leads to numerous interesting predictions, including: non-locality, generalization of the uncertainty relations, algebra deformations, constraining of the maximal occupation number, shifting of the vacuum energy and renormalization of the charge and speed of propagation of field excitations. Furthermore, a compact field space is a natural way to implement the "Principle of finiteness" of physical theories, which once motivated the Born-Infeld theory. Thus the presented framework has a variety of potential applications in the theories of fundamental interactions (e.g. quantum gravity), as well as in condensed matter physics (e.g. continuous spin chains), and can shed new light on the issue of divergences in quantum field theories.
The Theory of Conceptual Fields
ERIC Educational Resources Information Center
Vergnaud, Gerard
2009-01-01
The theory of conceptual fields is a developmental theory. It has two aims: (1) to describe and analyse the progressive complexity, on a long- and medium-term basis, of the mathematical competences that students develop inside and outside school, and (2) to establish better connections between the operational form of knowledge, which consists in…
Introducing Group Theory through Music
ERIC Educational Resources Information Center
Johnson, Craig M.
2009-01-01
The central ideas of postcalculus mathematics courses offered in college are difficult to introduce in middle and secondary schools, especially through the engineering and sciences examples traditionally used in algebra, geometry, and trigonometry textbooks. However, certain concepts in music theory can be used to expose students to interesting…
Double field theory inspired cosmology
Wu, Houwen; Yang, Haitang E-mail: hyanga@scu.edu.cn
2014-07-01
Double field theory proposes a generalized spacetime action possessing manifest T-duality on the level of component fields. We calculate the cosmological solutions of double field theory with vanishing Kalb-Ramond field. It turns out that double field theory provides a more consistent way to construct cosmological solutions than the standard string cosmology. We construct solutions for vanishing and non-vanishing symmetry preserving dilaton potentials. The solutions assemble the pre- and post-big bang evolutions in one single line element. Our results show a smooth evolution from an anisotropic early stage to an isotropic phase without any special initial conditions in contrast to previous models. In addition, we demonstrate that the contraction of the dual space automatically leads to both an inflation phase and a decelerated expansion of the ordinary space during different evolution stages.
String theory in electromagnetic fields
NASA Astrophysics Data System (ADS)
Ambjørn, Jan; Makeenko, Yuri M.; Semenoff, Gordon W.; Szabo, Richard J.
2003-02-01
A review of various aspects of superstrings in background electromagnetic fields is presented. Topics covered include the Born-Infeld action, spectrum of open strings in background gauge fields, the Schwinger mechanism, finite-temperature formalism and Hagedorn behaviour in external fields, Debye screening, D-brane scattering, thermodynamics of D-branes, and noncommutative field and string theories on D-branes. The electric field instabilities are emphasized throughout and contrasted with the case of magnetic fields. A new derivation of the velocity-dependent potential between moving D-branes is presented, as is a new result for the velocity corrections to the one-loop thermal effective potential.
Understanding conformal field theory through parafermions and Chern Simons theory
Hotes, S.A.
1992-11-19
Conformal field theories comprise a vast class of exactly solvable two dimensional quantum field theories. Conformal theories with an enlarged symmetry group, the current algebra symmetry, axe a key ingredient to possible string compactification models. The following work explores a Lagrangian approach to these theories. In the first part of this thesis, a large class of conformal theories, the so-called coset models, are derived semi-classically from a gauged version Of the Wess-Zumino-Witten functional. A non-local field transformation to the parafermionic field description is employed in the quantization procedure. Classically, these parafermionic fields satisfy non-trivial Poisson brackets, providing insight into the fractional spin nature of the conformal theory. The W-algebra symmetry is shown to appear naturally in this approach. In the second part of this thesis, the connection between the fusion algebra structure of Wess-Zumino-Witten models and the quantization of the Chern-Simons action on the torus is made explicit. The modular properties of the conformal model are also derived in this context, giving a natural demonstration of the Verlinde conjecture. The effects of background gauge fields and monopoles are also discussed.
Nonlocal and quasilocal field theories
NASA Astrophysics Data System (ADS)
Tomboulis, E. T.
2015-12-01
We investigate nonlocal field theories, a subject that has attracted some renewed interest in connection with nonlocal gravity models. We study, in particular, scalar theories of interacting delocalized fields, the delocalization being specified by nonlocal integral kernels. We distinguish between strictly nonlocal and quasilocal (compact support) kernels and impose conditions on them to insure UV finiteness and unitarity of amplitudes. We study the classical initial value problem for the partial integro-differential equations of motion in detail. We give rigorous proofs of the existence but accompanying loss of uniqueness of solutions due to the presence of future, as well as past, "delays," a manifestation of acausality. In the quantum theory we derive a generalization of the Bogoliubov causality condition equation for amplitudes, which explicitly exhibits the corrections due to nonlocality. One finds that, remarkably, for quasilocal kernels all acausal effects are confined within the compact support regions. We briefly discuss the extension to other types of fields and prospects of such theories.
Renormalizability of supersymmetric group field cosmology
NASA Astrophysics Data System (ADS)
Upadhyay, Sudhaker
2014-03-01
In this paper we consider the gauge invariant third quantized model of supersymmetric group field cosmology. The supersymmetric BRST invariance for such theory in non-linear gauge is also analysed. The path integral formulation to the case of a multiverse made up of homogeneous and isotropic spacetimes filled with a perfect fluid is presented. The renormalizability for the scattering of universes in multiverse are established with suitably constructed master equations for connected diagrams and proper vertices. The Slavnov-Taylor identities for this theory hold to all orders of radiative corrections.
Applications of Group Theory to Atoms, Molecules, and Solids
NASA Astrophysics Data System (ADS)
Wolfram, Thomas; Ellialtıǧlu, Şinasi
2014-01-01
Preface; 1. Introductory example: squarene; 2. Molecular vibrations of isotopically substituted AB2 molecules; 3. Spherical symmetry and the full rotation group; 4. Crystal field theory; 5. Electron spin and angular momentum; 6. Molecular electronic structure: the LCAO model; 7. Electronic states of diatomic molecules; 8. Transition metal complexes; 9. Space groups and crystalline solids; 10. Application of space group theory: energy bands for the perovskite structure; 11. Applications of space group theory: lattice vibrations; 12. Time reversal and magnetic groups; 13. Graphene; 14. Carbon nanotubes; Appendixes; Index.
Exceptional field theory: SO(5,5)
NASA Astrophysics Data System (ADS)
Abzalov, Aidar; Bakhmatov, Ilya; Musaev, Edvard T.
2015-06-01
We construct Exceptional Field Theory for the group SO(5, 5) based on the extended (6+16)-dimensional spacetime, which after reduction gives the maximal D = 6 supergravity. We present both a true action and a duality-invariant pseudo-action formulations. All the fields of the theory depend on the complete extended spacetime. The U-duality group SO(5, 5) is made a geometric symmetry of the theory by virtue of introducing the generalised Lie derivative that incorporates a duality transformation. Tensor hierarchy appears as a natural consequence of the algebra of generalised Lie derivatives that are viewed as gauge transformations. Upon truncating different subsets of the extra coordinates, maximal supergravities in D = 11 and D = 10 (type IIB) can be recovered from this theory.
Fornace, Mark E; Lee, Joonho; Miyamoto, Kaito; Manby, Frederick R; Miller, Thomas F
2015-02-10
We introduce embedded mean-field theory (EMFT), an approach that flexibly allows for the embedding of one mean-field theory in another without the need to specify or fix the number of particles in each subsystem. EMFT is simple, is well-defined without recourse to parameters, and inherits the simple gradient theory of the parent mean-field theories. In this paper, we report extensive benchmarking of EMFT for the case where the subsystems are treated using different levels of Kohn-Sham theory, using PBE or B3LYP/6-31G* in the high-level subsystem and LDA/STO-3G in the low-level subsystem; we also investigate different levels of density fitting in the two subsystems. Over a wide range of chemical problems, we find EMFT to perform accurately and stably, smoothly converging to the high-level of theory as the active subsystem becomes larger. In most cases, the performance is at least as good as that of ONIOM, but the advantages of EMFT are highlighted by examples that involve partitions across multiple bonds or through aromatic systems and by examples that involve more complicated electronic structure. EMFT is simple and parameter free, and based on the tests provided here, it offers an appealing new approach to a multiscale electronic structure.
Resummation in hot field theories
Andersen, Jens O. . E-mail: jensoa@nordita.dk; Strickland, Michael . E-mail: mike@hep.itp.tuwien.ac.at
2005-06-01
There has been significant progress in our understanding of finite-temperature field theory over the past decade. In this paper, we review the progress in perturbative thermal field theory focusing on thermodynamic quantities. We first discuss the breakdown of naive perturbation theory at finite temperature and the need for an effective expansion that resums an infinite class of diagrams in the perturbative expansion. This effective expansion which is due to Braaten and Pisarski, can be used to systematically calculate various static and dynamical quantities as a weak-coupling expansion in powers of g. However, it turns out that the weak-coupling expansion for thermodynamic quantities are useless unless the coupling constant is very small. We critically discuss various ways of reorganizing the perturbative series for thermal field theories in order to improve its convergence. These include screened perturbation theory (SPT), hard-thermal-loop perturbation theory, the {phi}-derivable approach, dimensionally reduced (DR) SPT, and the DR {phi}-derivable approach.
Gauge theory of a group of diffeomorphisms. II. The conformal and de Sitter groups
NASA Astrophysics Data System (ADS)
Lord, Eric A.
1986-12-01
The extension of Hehl's Poincaré gauge theory to more general groups that include space-time diffeomorphisms is worked out for two particular examples, one corresponding to the action of the conformal group on Minkowski space, and the other to the action of the de Sitter group on de Sitter space, and the effect of these groups on physical fields.
Transpersonal Group Psychotherapy: Theory, Method, and Community.
ERIC Educational Resources Information Center
Clark, Carlton F. "Perk"
1998-01-01
Transpersonal group psychotherapy is a carpet of theory, technique, and experiences woven from threads of contemporary psychology, mysticism, and a perennial philosophy many centuries old. Introduces the basic concepts of transpersonal group psychotherapy, proposes a model of transpersonal group psychotherapy, discusses the training of…
Noncommutative Geometry in M-Theory and Conformal Field Theory
Morariu, Bogdan
1999-05-01
In the first part of the thesis I will investigate in the Matrix theory framework, the subgroup of dualities of the Discrete Light Cone Quantization of M-theory compactified on tori, which corresponds to T-duality in the auxiliary Type II string theory. After a review of matrix theory compactification leading to noncommutative supersymmetric Yang-Mills gauge theory, I will present solutions for the fundamental and adjoint sections on a two-dimensional twisted quantum torus and generalize to three-dimensional twisted quantum tori. After showing how M-theory T-duality is realized in supersymmetric Yang-Mills gauge theories on dual noncommutative tori I will relate this to the mathematical concept of Morita equivalence of C*-algebras. As a further generalization, I consider arbitrary Ramond-Ramond backgrounds. I will also discuss the spectrum of the toroidally compactified Matrix theory corresponding to quantized electric fluxes on two and three tori. In the second part of the thesis I will present an application to conformal field theory involving quantum groups, another important example of a noncommutative space. First, I will give an introduction to Poisson-Lie groups and arrive at quantum groups using the Feynman path integral. I will quantize the symplectic leaves of the Poisson-Lie group SU(2)*. In this way we obtain the unitary representations of U{sub q}(SU(2)). I discuss the X-structure of SU(2)* and give a detailed description of its leaves using various parametrizations. Then, I will introduce a new reality structure on the Heisenberg double of Fun{sub q} (SL(N,C)) for q phase, which can be interpreted as the quantum phase space of a particle on the q-deformed mass-hyperboloid. I also present evidence that the above real form describes zero modes of certain non-compact WZNW-models.
Variational methods for field theories
NASA Astrophysics Data System (ADS)
Ben-Menahem, Shahar
1986-09-01
The thesis is presented in four parts dealing with field theory models: Periodic Quantum Electrodynamics (PQED) in (2+1) dimensions, free scalar field theory in (1+1) dimensions, the Quantum XY model in (1+1) dimensions, and the (1+1) dimensional Ising model in a transverse magnetic field. The last three parts deal exclusively with variational methods; the PQED part involves mainly the path integral approach. The PQED calculation results in a better understanding of the connection between electric confinement through monopole screening, and confinement through tunneling between degenerate vacua. Free field theory is used as a laboratory for a new variational blocking truncation approximation, in which the high frequency modes in a block are truncated to wave functions that depend on the slower background model (Born Oppenheimer approximation). For the XY model, several trial wave functions for the ground state are explored, with an emphasis on the periodic Gaussian. In the 4th part, the transfer matrix method is used to find a good (non blocking) trial ground state for the Ising model in a transverse magnetic field in (1+1) dimensions.
Theory Loves Practice: A Teacher Researcher Group
ERIC Educational Resources Information Center
Hochtritt, Lisa; Thulson, Anne; Delaney, Rachael; Dornbush, Talya; Shay, Sarah
2014-01-01
Once a month, art educators from the Denver metro area have been gathering together in the spirit of inquiry to explore issues of the perceived theory and daily practice divide. The Theory Loves Practice (TLP) group was started in 2010 by Professors Rachael Delaney and Anne Thulson from Metropolitan State University of Denver (MSU) and now has 40…
Introduction to string theory and conformal field theory
Belavin, A. A. Tarnopolsky, G. M.
2010-05-15
A concise survey of noncritical string theory and two-dimensional conformal field theory is presented. A detailed derivation of a conformal anomaly and the definition and general properties of conformal field theory are given. Minimal string theory, which is a special version of the theory, is considered. Expressions for the string susceptibility and gravitational dimensions are derived.
Bohmian mechanics and quantum field theory.
Dürr, Detlef; Goldstein, Sheldon; Tumulka, Roderich; Zanghì, Nino
2004-08-27
We discuss a recently proposed extension of Bohmian mechanics to quantum field theory. For more or less any regularized quantum field theory there is a corresponding theory of particle motion, which, in particular, ascribes trajectories to the electrons or whatever sort of particles the quantum field theory is about. Corresponding to the nonconservation of the particle number operator in the quantum field theory, the theory describes explicit creation and annihilation events: the world lines for the particles can begin and end.
Variational methods for field theories
Ben-Menahem, S.
1986-09-01
Four field theory models are studied: Periodic Quantum Electrodynamics (PQED) in (2 + 1) dimensions, free scalar field theory in (1 + 1) dimensions, the Quantum XY model in (1 + 1) dimensions, and the (1 + 1) dimensional Ising model in a transverse magnetic field. The last three parts deal exclusively with variational methods; the PQED part involves mainly the path-integral approach. The PQED calculation results in a better understanding of the connection between electric confinement through monopole screening, and confinement through tunneling between degenerate vacua. This includes a better quantitative agreement for the string tensions in the two approaches. Free field theory is used as a laboratory for a new variational blocking-truncation approximation, in which the high-frequency modes in a block are truncated to wave functions that depend on the slower background modes (Boron-Oppenheimer approximation). This ''adiabatic truncation'' method gives very accurate results for ground-state energy density and correlation functions. Various adiabatic schemes, with one variable kept per site and then two variables per site, are used. For the XY model, several trial wave functions for the ground state are explored, with an emphasis on the periodic Gaussian. A connection is established with the vortex Coulomb gas of the Euclidean path integral approach. The approximations used are taken from the realms of statistical mechanics (mean field approximation, transfer-matrix methods) and of quantum mechanics (iterative blocking schemes). In developing blocking schemes based on continuous variables, problems due to the periodicity of the model were solved. Our results exhibit an order-disorder phase transition. The transfer-matrix method is used to find a good (non-blocking) trial ground state for the Ising model in a transverse magnetic field in (1 + 1) dimensions.
Group Theory of Covariant Harmonic Oscillators
ERIC Educational Resources Information Center
Kim, Y. S.; Noz, Marilyn E.
1978-01-01
A simple and concrete example for illustrating the properties of noncompact groups is presented. The example is based on the covariant harmonic-oscillator formalism in which the relativistic wave functions carry a covariant-probability interpretation. This can be used in a group theory course for graduate students who have some background in…
A Review of Group Systems Theory
ERIC Educational Resources Information Center
Connors, Joanie V.; Caple, Richard B.
2005-01-01
The ability to see interpersonal and group processes beyond the individual level is an essential skill for group therapists (Crouch, Bloch & Wanlass, 1994; Dies, 1994; Fuhriman & Burlingame, 1994). In addition to interpersonal therapy models (e.g., Sullivan and Yalom), there are a number of systems theory models that offer a broad array of…
A Lagrangian effective field theory
Vlah, Zvonimir; White, Martin; Aviles, Alejandro
2015-09-02
We have continued the development of Lagrangian, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be formulated in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The `new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all of our models fare well on scales larger than about two to three times the non-linear scale, but fail as the non-linear scale is approached. This is slightly less reach than has been seen previously. At low redshift the Lagrangian model fares as well as EFT in its Eulerian formulation, but at higher z the Eulerian EFT fits the data to smaller scales than resummed, Lagrangian EFT. Furthermore, all the perturbative models fare better than linear theory.
A Lagrangian effective field theory
Vlah, Zvonimir; White, Martin; Aviles, Alejandro
2015-09-02
We have continued the development of Lagrangian, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be formulated in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The `new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all ofmore » our models fare well on scales larger than about two to three times the non-linear scale, but fail as the non-linear scale is approached. This is slightly less reach than has been seen previously. At low redshift the Lagrangian model fares as well as EFT in its Eulerian formulation, but at higher z the Eulerian EFT fits the data to smaller scales than resummed, Lagrangian EFT. Furthermore, all the perturbative models fare better than linear theory.« less
A Lagrangian effective field theory
Vlah, Zvonimir; White, Martin; Aviles, Alejandro E-mail: mwhite@berkeley.edu
2015-09-01
We have continued the development of Lagrangian, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be formulated in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The 'new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all of our models fare well on scales larger than about two to three times the non-linear scale, but fail as the non-linear scale is approached. This is slightly less reach than has been seen previously. At low redshift the Lagrangian model fares as well as EFT in its Eulerian formulation, but at higher z the Eulerian EFT fits the data to smaller scales than resummed, Lagrangian EFT. All the perturbative models fare better than linear theory.
Coherent states formulation of polymer field theory
Man, Xingkun; Villet, Michael C.; Delaney, Kris T.; Orland, Henri; Fredrickson, Glenn H.
2014-01-14
We introduce a stable and efficient complex Langevin (CL) scheme to enable the first direct numerical simulations of the coherent-states (CS) formulation of polymer field theory. In contrast with Edwards’ well-known auxiliary-field (AF) framework, the CS formulation does not contain an embedded nonlinear, non-local, implicit functional of the auxiliary fields, and the action of the field theory has a fully explicit, semi-local, and finite-order polynomial character. In the context of a polymer solution model, we demonstrate that the new CS-CL dynamical scheme for sampling fluctuations in the space of coherent states yields results in good agreement with now-standard AF-CL simulations. The formalism is potentially applicable to a broad range of polymer architectures and may facilitate systematic generation of trial actions for use in coarse-graining and numerical renormalization-group studies.
Group Chaos Theory: A Metaphor and Model for Group Work
ERIC Educational Resources Information Center
Rivera, Edil Torres; Wilbur, Michael; Frank-Saraceni, James; Roberts-Wilbur, Janice; Phan, Loan T.; Garrett, Michael T.
2005-01-01
Group phenomena and interactions are described through the use of the chaos theory constructs and characteristics of sensitive dependence on initial conditions, phase space, turbulence, emergence, self-organization, dissipation, iteration, bifurcation, and attractors and fractals. These constructs and theoretical tenets are presented as applicable…
Rearranging Pionless Effective Field Theory
Martin Savage; Silas Beane
2001-11-19
We point out a redundancy in the operator structure of the pionless effective field theory which dramatically simplifies computations. This redundancy is best exploited by using dibaryon fields as fundamental degrees of freedom. In turn, this suggests a new power counting scheme which sums range corrections to all orders. We explore this method with a few simple observables: the deuteron charge form factor, n p -> d gamma, and Compton scattering from the deuteron. Higher dimension operators involving electroweak gauge fields are not renormalized by the s-wave strong interactions, and therefore do not scale with inverse powers of the renormalization scale. Thus, naive dimensional analysis of these operators is sufficient to estimate their contribution to a given process.
Quantum field theories on manifolds with curved boundaries: Scalar fields
NASA Astrophysics Data System (ADS)
McAvity, D. M.; Osborn, H.
1993-04-01
A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the Green function for second-order differential operators valid in the neighbourhood of the boundary and which is obtained from a corresponding expansion of the associated heat kernel derived earlier for arbitrary mixed Dirichlet and Neumann boundary conditions. The first few leading terms in the expansion are sufficient to calculate all additional divergences present in a perturbative loop expansion as a consequence of the presence of the boundary. The method is applied to a general renormalisable scalar field theory in four dimensions using dimensional regularisation to two loops and expanding about arbitrary background fields. Detailed results are also specialised to an O( n) symmetric model with a single coupling constant. Extra boundary terms are introduced into the action which give rise to either Dirichlet orgeneralized Neumann boundary conditions for the quantum fields. For plane boundaries the resulting renormalisation group functions are in accord with earlier results but here the additional terms depending on the extrinsic curvature of the boundary are found. Various consistency relations are also checked and the implications of conformal invariance at the critical point where the β-function vanishes are also derived. For a general scalar field theory, where the fieldsø attain specified values ϕ in the boundary, the local Schrödinger equation for the wave functional defined by the functional integral under deformations of the boundary is also verified to two loops. The perturbative expansion for the wave functional is defined by expansion around the solution of the classical field equations satisfying the required boundary values and the counterterms necessary to derive a finite hamiltonian operator, which includes a functional Laplace operator on the fields ϕ, are
A Field Theory Problem Relating to Questions in Hyperfield Theory
NASA Astrophysics Data System (ADS)
Massouros, Ch. G.
2011-09-01
M. Krasner introduced the notions of the hypefield and the hyperring in 1956. Much later, he constructed the quotient hyperfield/hyperrring, using a field/ring and a subgroup of its multiplicative group/semigroup. The existence of non-quotient hyperfields and hyperrings was an essential question for the self-sufficiency of the theory of hyperfields and hyperrings vis-à-vis that of fields and rings. The momogene hyperfield, which was introduced by the author, is a hyperfield H having the property x - x = H for all x≠0. The existence of non-quotient monogene hyperfields is a hitherto open question. The answer to this question is directly connected with the answer to the question which fields can be expressed as a difference of a subgroup of their multiplicative group from itself and which these subgroups are. These issues, as well as some relevant theorems are presented in this paper.
Could reggeon field theory be an effective theory for QCD in the Regge limit?
NASA Astrophysics Data System (ADS)
Bartels, Jochen; Contreras, Carlos; Vacca, G. P.
2016-03-01
In this paper we investigate the possibility whether, in the extreme limit of high energies and large transverse distances, reggeon field theory might serve as an effective theory of high energy scattering for strong interactions. We analyse the functional renormalization group equations (flow equations) of reggeon field theory and search for fixed points in the space of (local) reggeon field theories. We study in complementary ways the candidate for the scaling solution, investigate its main properties and briefly discuss possible physical interpretations.
Effective Field Theory for Jet Processes.
Becher, Thomas; Neubert, Matthias; Rothen, Lorena; Shao, Ding Yu
2016-05-13
Processes involving narrow jets receive perturbative corrections enhanced by logarithms of the jet opening angle and the ratio of the energies inside and outside the jets. Analyzing cone-jet processes in effective field theory, we find that in addition to soft and collinear fields their description requires degrees of freedom that are simultaneously soft and collinear to the jets. These collinear-soft particles can resolve individual collinear partons, leading to a complicated multi-Wilson-line structure of the associated operators at higher orders. Our effective field theory provides, for the first time, a factorization formula for a cone-jet process, which fully separates the physics at different energy scales. Its renormalization-group equations control all logarithmically enhanced higher-order terms, in particular also the nonglobal logarithms.
Integrable structures in quantum field theory
NASA Astrophysics Data System (ADS)
Negro, Stefano
2016-08-01
This review was born as notes for a lecture given at the Young Researchers Integrability School (YRIS) school on integrability in Durham, in the summer of 2015. It deals with a beautiful method, developed in the mid-nineties by Bazhanov, Lukyanov and Zamolodchikov and, as such, called BLZ. This method can be interpreted as a field theory version of the quantum inverse scattering, also known as the algebraic Bethe ansatz. Starting with the case of conformal field theories (CFTs) we show how to build the field theory analogues of commuting transfer T matrices and Baxter Q-operators of integrable lattice models. These objects contain the complete information of the integrable structure of the theory, viz. the integrals of motion, and can be used, as we will show, to derive the thermodynamic Bethe ansatz and nonlinear integral equations. This same method can be easily extended to the description of integrable structures of certain particular massive deformations of CFTs; these, in turn, can be described as quantum group reductions of the quantum sine-Gordon model and it is an easy step to include this last theory in the framework of BLZ approach. Finally we show an interesting and surprising connection of the BLZ structures with classical objects emerging from the study of classical integrable models via the inverse scattering transform method. This connection goes under the name of ODE/IM correspondence and we will present it for the specific case of quantum sine-Gordon model only.
Variational Methods for Field Theories.
NASA Astrophysics Data System (ADS)
Ben-Menahem, Shahar
The thesis has four parts, dealing with four field theory models: Periodic Quantum Electrodynamics (PQED) in (2 + 1) dimensions, free scalar field theory in (1 + 1) dimensions, the Quantum XY model in (1 + 1) dimensions, and the (1 + 1) dimensional Ising model in a transverse magnetic field. The last three parts deal exclusively with variational methods; the PQED part involves mainly the path-integral approach. The PQED calculation results in a better understanding of the connection between electric confinement through monopole screening, and confinement through tunneling between degenerate vacua. This includes a better quantitative agreement for the string tensions in the two approaches. In the second part, we use free field theory as a loboratory for a new variational blocking-tuncation approximation, in which the high-frequency modes in a block are truncated to wave functions that depend on the slower background modes(Born-Oppenheimer approximation). This "adiabatic truncation" method gives very accurate results for ground -state energy density and correlation functions. Without the adiabatic method, a much larger number of state per block must be kept to get comparable results. Various adiabatic schemes, with one variable kept per site and then two variables per site, are used. For the XY model, several trial wave functions for the ground state are explored, with an emphasis on the periodic Gaussian. A connection is established with the vortex Coulomb gas of the Eclidean path integral approach. The approximations used are taken from the realms of statistical mechanics (mean field approximation, transfer-matrix methods) and of quantum mechanics (iterative blocking schemes). In developing blocking schemes based on continuous variables, problems due to the periodicity of the model were solved. Our results exhibit an order-disorder phase transition. This transition is a rudimentary version of the actual transition known to occur in the XY model, and is
Transport theory of massless fields
Mrowczynski, S. |
1997-08-01
Using the Schwinger-Keldysh technique we discuss how to derive the transport equations for the system of massless quantum fields. We analyze the scalar field models with quartic and cubic interaction terms. In the {phi}{sup 4} model the massive quasiparticles appear due to the self-interaction of massless bare fields. Therefore, the derivation of the transport equations strongly resembles one of the massive fields, but the subset of diagrams which provides the quasiparticle mass has to be resummed. The kinetic equation for the finite width quasiparticles is found, where, except for the mean-field and collision terms, there are terms which are absent in the standard Boltzmann equation. The structure of these terms is discussed. In the massless {phi}{sup 3} model the massive quasiparticles do not emerge and presumably there is no transport theory corresponding to this model. It is not surprising since the {phi}{sup 3} model is, in any case, ill defined. {copyright} {ital 1997} {ital The American Physical Society}
Haag's theorem in noncommutative quantum field theory
Antipin, K. V.; Mnatsakanova, M. N.; Vernov, Yu. S.
2013-08-15
Haag's theorem was extended to the general case of noncommutative quantum field theory when time does not commute with spatial variables. It was proven that if S matrix is equal to unity in one of two theories related by unitary transformation, then the corresponding one in the other theory is equal to unity as well. In fact, this result is valid in any SO(1, 1)-invariant quantum field theory, an important example of which is noncommutative quantum field theory.
Topics in low-dimensional field theory
Crescimanno, M.J.
1991-04-30
Conformal field theory is a natural tool for understanding two- dimensional critical systems. This work presents results in the lagrangian approach to conformal field theory. The first sections are chiefly about a particular class of field theories called coset constructions and the last part is an exposition of the connection between two-dimensional conformal theory and a three-dimensional gauge theory whose lagrangian is the Chern-Simons density.
Teaching Group Theory Using Rubik's Cubes
ERIC Educational Resources Information Center
Cornock, Claire
2015-01-01
Being situated within a course at the applied end of the spectrum of maths degrees, the pure mathematics modules at Sheffield Hallam University have an applied spin. Pure topics are taught through consideration of practical examples such as knots, cryptography and automata. Rubik's cubes are used to teach group theory within a final year pure…
Large gauge transformations in double field theory
NASA Astrophysics Data System (ADS)
Hohm, Olaf; Zwiebach, Barton
2013-02-01
Finite gauge transformations in double field theory can be defined by the exponential of generalized Lie derivatives. We interpret these transformations as `generalized coordinate transformations' in the doubled space by proposing and testing a formula that writes large transformations in terms of derivatives of the coordinate maps. Successive generalized coordinate transformations give a generalized coordinate transformation that differs from the direct composition of the original two. Instead, it is constructed using the Courant bracket. These transformations form a group when acting on fields but, intriguingly, do not associate when acting on coordinates.
Quantum Field Theory in (0 + 1) Dimensions
ERIC Educational Resources Information Center
Boozer, A. D.
2007-01-01
We show that many of the key ideas of quantum field theory can be illustrated simply and straightforwardly by using toy models in (0 + 1) dimensions. Because quantum field theory in (0 + 1) dimensions is equivalent to quantum mechanics, these models allow us to use techniques from quantum mechanics to gain insight into quantum field theory. In…
Studies in Quantum Field Theory
NASA Astrophysics Data System (ADS)
Bastianelli, Fiorenzo
We analyze several topics in quantum field theory, mainly motivated by their role in the formulation of string theories. The common theme in what follows is the implementation of symmetries, such as local supersymmetry or BRST symmetry, through an action principle and the analysis of anomalies, the latter describing the breakdown of these symmetries at the quantum level. In the first part of this dissertation, we analyze "chiral bosons", i.e. massless scalar fields in a two -dimensional spacetime propagating in only one of the two light-cone directions. We present a general method for constructing couplings for chiral bosons and give details for the coupling to supergravity. The notion of a two dimensional chiral boson is generalized in d = 4k + 2 spacetime dimensions to that of a self-dual antisymmetric tensor field. We derive the coupling to gravity and compute the gravitational anomalies using the Feynman rules obtained from the action. We find agreement with the important work of Alvarez-Gaume and Witten, who conjectured the relevant Feynman rules. Our result therefore completes and justifies the Alvarez-Gaume-Witten findings. For the case of d = 2 we also show how to use the method of Fujikawa for computing anomalies from the non-invariance of the path integral measure. We obtain the full effective action by integrating the anomaly equation. In the second part we focus on a method for computing the consistent anomalies in the Fujikawa scheme. In a first application, we derive the consistent regulators for the various fields of the quantum action of the spinning string in superspace. These regulators produce the anomalies which satisfy the Wess-Zumino consistency conditions. In a second application, we analyze the anomalous structure of the Green-Schwarz formulation of the heterotic string. We find anomalies which generically do not cancel on an arbitrary world-sheet manifold. This raises questions concerning the possible validity of such a formulation of
Logarithmic conformal field theory: beyond an introduction
NASA Astrophysics Data System (ADS)
Creutzig, Thomas; Ridout, David
2013-12-01
of the underlying chiral algebra and the modular data pertaining to the characters of the representations. Each of the archetypal logarithmic conformal field theories is studied here by first determining its irreducible spectrum, which turns out to be continuous, as well as a selection of natural reducible, but indecomposable, modules. This is followed by a detailed description of how to obtain character formulae for each irreducible, a derivation of the action of the modular group on the characters, and an application of the Verlinde formula to compute the Grothendieck fusion rules. In each case, the (genuine) fusion rules are known, so comparisons can be made and favourable conclusions drawn. In addition, each example admits an infinite set of simple currents, hence extended symmetry algebras may be constructed and a series of bulk modular invariants computed. The spectrum of such an extended theory is typically discrete and this is how the triplet model \\mathfrak {W} (1,2) arises, for example. Moreover, simple current technology admits a derivation of the extended algebra fusion rules from those of its continuous parent theory. Finally, each example is concluded by a brief description of the computation of some bulk correlators, a discussion of the structure of the bulk state space, and remarks concerning more advanced developments and generalizations. The final part gives a very short account of the theory of staggered modules, the (simplest class of) representations that are responsible for the logarithmic singularities that distinguish logarithmic theories from their rational cousins. These modules are discussed in a generality suitable to encompass all the examples met in this review and some of the very basic structure theory is proven. Then, the important quantities known as logarithmic couplings are reviewed for Virasoro staggered modules and their role as fundamentally important parameters, akin to the three-point constants of rational conformal field
Instantons in Lifshitz field theories
NASA Astrophysics Data System (ADS)
Fujimori, Toshiaki; Nitta, Muneto
2015-10-01
BPS instantons are discussed in Lifshitz-type anisotropic field theories. We consider generalizations of the sigma model/Yang-Mills instantons in renormalizable higher dimensional models with the classical Lifshitz scaling invariance. In each model, BPS instanton equation takes the form of the gradient flow equations for "the superpotential" defining "the detailed balance condition". The anisotropic Weyl rescaling and the coset space dimensional reduction are used to map rotationally symmetric instantons to vortices in two-dimensional anisotropic systems on the hyperbolic plane. As examples, we study anisotropic BPS baby Skyrmion 1+1 dimensions and BPS Skyrmion in 2+1 dimensions, for which we take Kähler 1-form and the Wess-Zumiono-Witten term as the superpotentials, respectively, and an anisotropic generalized Yang-Mills instanton in 4 + 1 dimensions, for which we take the Chern-Simons term as the superpotential.
Matrix field theory: Applications to superconductivity
NASA Astrophysics Data System (ADS)
Zhou, Lubo
In this thesis a systematic, functional matrix field theory is developed to describe both clean and disordered s-wave and d-wave superconductors and the quantum phase transitions associated with them. The thesis can be divided into three parts. The first part includes chapters 1 to 3. In chapter one a general physical introduction is given. In chapters two and three the theory is developed and used to compute the equation of state as well as the number-density susceptibility, spin-density susceptibility, the sound attenuation coefficient, and the electrical conductivity in both clean and disordered s-wave superconductors. The second part includes chapter four. In this chapter we use the theory to describe the disorder-induced metal - superconductor quantum phase transition. The key physical idea here is that in addition to the superconducting order-parameter fluctuations, there are also additional soft fermionic fluctuations that are important at the transition. We develop a local field theory for the coupled fields describing superconducting and soft fermionic fluctuations. Using simple renormalization group and scaling ideas, we exactly determine the critical behavior at this quantum phase transition. Our theory justifies previous approaches. The third part includes chapter five. In this chapter we study the analogous quantum phase transition in disordered d-wave superconductors. This theory should be related to high Tc superconductors. Surprisingly, we show that in both the underdoped and overdoped regions, the coupling of superconducting fluctuations to the soft disordered fermionic fluctuations is much weaker than that in the s-wave case. The net result is that the disordered quantum phase transition in this case is a strong coupling, or described by an infinite disordered fixed point, transition and cannot be described by the perturbative RG description that works so well in the s-wave case. The transition appears to be related to the one that occurs in
Palmer, R.B.; Baggett, N.; Claus, J.; Fernow, R.; Stumer, I.; Figueroa, H.; Kroll, N.; Funk, W.; Lee-Whiting, G.; Pickup, M.
1985-04-01
Substantial progress since the Los Alamos Workshop two years ago is reported. A radio-frequency model of a grating accelerator has been tested at Cornell, and extensive calculations compared with observations. Alternative structures consisting of either hemispherical bumps on a plane, or conducting spheres in space, have also been rf modeled. The use of liquid droplets to form such structures has been proposed and a conceptual design studied. Calculations and experiments have examined the effects of surface plasmas, and shown that in this case the reflectivity is low. However, calculations and observations suggest that gradients in excess of 1 GeV/meter should be obtainable without forming such plasma. An examination of wake fields shows that, with Landau damping, these are independent of wavelength. The use of near field structures to act as high gradient focusing elements has been studied and shows promise, independent of the acceleration mechanism. A proposal has been made to establish a facility that would enable ''proof of principle experiments'' to be performed on these and other laser driven accelerator mechanisms. 11 refs., 10 figs.
Groups, information theory, and Einstein's likelihood principle
NASA Astrophysics Data System (ADS)
Sicuro, Gabriele; Tempesta, Piergiulio
2016-04-01
We propose a unifying picture where the notion of generalized entropy is related to information theory by means of a group-theoretical approach. The group structure comes from the requirement that an entropy be well defined with respect to the composition of independent systems, in the context of a recently proposed generalization of the Shannon-Khinchin axioms. We associate to each member of a large class of entropies a generalized information measure, satisfying the additivity property on a set of independent systems as a consequence of the underlying group law. At the same time, we also show that Einstein's likelihood function naturally emerges as a byproduct of our informational interpretation of (generally nonadditive) entropies. These results confirm the adequacy of composable entropies both in physical and social science contexts.
Groups, information theory, and Einstein's likelihood principle.
Sicuro, Gabriele; Tempesta, Piergiulio
2016-04-01
We propose a unifying picture where the notion of generalized entropy is related to information theory by means of a group-theoretical approach. The group structure comes from the requirement that an entropy be well defined with respect to the composition of independent systems, in the context of a recently proposed generalization of the Shannon-Khinchin axioms. We associate to each member of a large class of entropies a generalized information measure, satisfying the additivity property on a set of independent systems as a consequence of the underlying group law. At the same time, we also show that Einstein's likelihood function naturally emerges as a byproduct of our informational interpretation of (generally nonadditive) entropies. These results confirm the adequacy of composable entropies both in physical and social science contexts.
Groups, information theory, and Einstein's likelihood principle.
Sicuro, Gabriele; Tempesta, Piergiulio
2016-04-01
We propose a unifying picture where the notion of generalized entropy is related to information theory by means of a group-theoretical approach. The group structure comes from the requirement that an entropy be well defined with respect to the composition of independent systems, in the context of a recently proposed generalization of the Shannon-Khinchin axioms. We associate to each member of a large class of entropies a generalized information measure, satisfying the additivity property on a set of independent systems as a consequence of the underlying group law. At the same time, we also show that Einstein's likelihood function naturally emerges as a byproduct of our informational interpretation of (generally nonadditive) entropies. These results confirm the adequacy of composable entropies both in physical and social science contexts. PMID:27176234
Toward a gauge field theory of gravity.
NASA Astrophysics Data System (ADS)
Yilmaz, H.
Joint use of two differential identities (Bianchi and Freud) permits a gauge field theory of gravity in which the gravitational energy is localizable. The theory is compatible with quantum mechanics and is experimentally viable.
Towards weakly constrained double field theory
NASA Astrophysics Data System (ADS)
Lee, Kanghoon
2016-08-01
We show that it is possible to construct a well-defined effective field theory incorporating string winding modes without using strong constraint in double field theory. We show that X-ray (Radon) transform on a torus is well-suited for describing weakly constrained double fields, and any weakly constrained fields are represented as a sum of strongly constrained fields. Using inverse X-ray transform we define a novel binary operation which is compatible with the level matching constraint. Based on this formalism, we construct a consistent gauge transform and gauge invariant action without using strong constraint. We then discuss the relation of our result to the closed string field theory. Our construction suggests that there exists an effective field theory description for massless sector of closed string field theory on a torus in an associative truncation.
Group theoretical methods and wavelet theory: coorbit theory and applications
NASA Astrophysics Data System (ADS)
Feichtinger, Hans G.
2013-05-01
Before the invention of orthogonal wavelet systems by Yves Meyer1 in 1986 Gabor expansions (viewed as discretized inversion of the Short-Time Fourier Transform2 using the overlap and add OLA) and (what is now perceived as) wavelet expansions have been treated more or less at an equal footing. The famous paper on painless expansions by Daubechies, Grossman and Meyer3 is a good example for this situation. The description of atomic decompositions for functions in modulation spaces4 (including the classical Sobolev spaces) given by the author5 was directly modeled according to the corresponding atomic characterizations by Frazier and Jawerth,6, 7 more or less with the idea of replacing the dyadic partitions of unity of the Fourier transform side by uniform partitions of unity (so-called BUPU's, first named as such in the early work on Wiener-type spaces by the author in 19808). Watching the literature in the subsequent two decades one can observe that the interest in wavelets "took over", because it became possible to construct orthonormal wavelet systems with compact support and of any given degree of smoothness,9 while in contrast the Balian-Low theorem is prohibiting the existence of corresponding Gabor orthonormal bases, even in the multi-dimensional case and for general symplectic lattices.10 It is an interesting historical fact that* his construction of band-limited orthonormal wavelets (the Meyer wavelet, see11) grew out of an attempt to prove the impossibility of the existence of such systems, and the final insight was that it was not impossible to have such systems, and in fact quite a variety of orthonormal wavelet system can be constructed as we know by now. Meanwhile it is established wisdom that wavelet theory and time-frequency analysis are two different ways of decomposing signals in orthogonal resp. non-orthogonal ways. The unifying theory, covering both cases, distilling from these two situations the common group theoretical background lead to the
Conformal field theories from deformations of theories with Wn symmetry
NASA Astrophysics Data System (ADS)
Babaro, Juan Pablo; Giribet, Gaston; Ranjbar, Arash
2016-10-01
We construct a set of nonrational conformal field theories that consist of deformations of Toda field theory for s l (n ). In addition to preserving conformal invariance, the theories may still exhibit a remnant infinite-dimensional affine symmetry. The case n =3 is used to illustrate this phenomenon, together with further deformations that yield enhanced Kac-Moody symmetry algebras. For generic n we compute N -point correlation functions on the Riemann sphere and show that these can be expressed in terms of s l (n ) Toda field theory ((N -2 )n +2 ) -point correlation functions.
Special unitary groups in polarimetry theory
NASA Astrophysics Data System (ADS)
Cloude, Shane R.
1994-09-01
In this paper we consider application of the general theory of unitary matrices to the problem of wave propagation and scattering involving polarized waves. Having outlined useful parameterizations of these low dimensional matrix groups, we then develop a general processing strategy which we suggest is useful for the extraction of physical information from a range of scattering and propagation matrices in optics and radar. Examples are presented of application of the unitary matrix structure to the problems of absolute phase definition and random wave scattering.
Teaching group theory using Rubik's cubes
NASA Astrophysics Data System (ADS)
Cornock, Claire
2015-10-01
Being situated within a course at the applied end of the spectrum of maths degrees, the pure mathematics modules at Sheffield Hallam University have an applied spin. Pure topics are taught through consideration of practical examples such as knots, cryptography and automata. Rubik's cubes are used to teach group theory within a final year pure elective based on physical examples. Abstract concepts, such as subgroups, homomorphisms and equivalence relations are explored with the cubes first. In addition to this, conclusions about the cubes can be made through the consideration of algebraic approaches through a process of discovery. The teaching, learning and assessment methods are explored in this paper, along with the challenges and limitations of the methods. The physical use of Rubik's cubes within the classroom and examination will be presented, along with the use of peer support groups in this process. The students generally respond positively to the teaching methods and the use of the cubes.
Scalar field theory on noncommutative Snyder spacetime
Battisti, Marco Valerio; Meljanac, Stjepan
2010-07-15
We construct a scalar field theory on the Snyder noncommutative space-time. The symmetry underlying the Snyder geometry is deformed at the co-algebraic level only, while its Poincare algebra is undeformed. The Lorentz sector is undeformed at both the algebraic and co-algebraic level, but the coproduct for momenta (defining the star product) is non-coassociative. The Snyder-deformed Poincare group is described by a non-coassociative Hopf algebra. The definition of the interacting theory in terms of a nonassociative star product is thus questionable. We avoid the nonassociativity by the use of a space-time picture based on the concept of the realization of a noncommutative geometry. The two main results we obtain are (i) the generic (namely, for any realization) construction of the co-algebraic sector underlying the Snyder geometry and (ii) the definition of a nonambiguous self-interacting scalar field theory on this space-time. The first-order correction terms of the corresponding Lagrangian are explicitly computed. The possibility to derive Noether charges for the Snyder space-time is also discussed.
Chern-Simons theory with finite gauge group
NASA Astrophysics Data System (ADS)
Freed, Daniel S.; Quinn, Frank
1993-10-01
We construct in detail a 2+1 dimensional gauge field theory with finite gauge group. In this case the path integral reduces to a finite sum, so there are no analytic problems with the quantization. The theory was originally introduced by Dijkgraaf and Witten without details. The point of working it out carefully is to focus on the algebraic structure, and particularly the construction of quantum Hilbert spaces on closed surfaces by cutting and pasting. This includes the “Verlinde formula”. The careful development may serve as a model for dealing with similar issues in more complicated cases.
Boson formulation of fermion field theories
Ha, Y.K.
1984-04-15
The nonperturbative connection between a canonical Fermi field and a canonical Bose field in two dimensions is developed and its validity verified according to the tenets of quantum field theory. We advocate the point of view that a boson formulation offers a unifying theme in understanding the structure of many theories. This is illustrated by the boson formulation of a multifermion theory with chiral and internal symmetries. Many features of the massless theory, such as dynamical mass generation with asymptotic-freedom behavior, hidden chiral symmetry, and connections with models of apparently different internal symmetries, are readily transparent through such fermion-boson metamorphosis.
Remnant group of local Lorentz transformations in f (T ) theories
NASA Astrophysics Data System (ADS)
Ferraro, Rafael; Fiorini, Franco
2015-03-01
It is shown that the extended teleparallel gravitational theories, known as f (T ) theories, inherit some on shell local Lorentz invariance associated with the tetrad field defining the spacetime structure. We discuss some enlightening examples, such as Minkowski spacetime and cosmological (Friedmann-Robertson-Walker and Bianchi type I) manifolds. In the first case, we show that the absence of gravity reveals itself as an incapability in the selection of a preferred parallelization at a local level, due to the fact that the infinitesimal local Lorentz subgroup acts as a symmetry group of the frame characterizing Minkowski spacetime. Finite transformations are also discussed in these examples and, contrary to the common lore on the subject, we conclude that the set of tetrads responsible for the parallelization of these manifolds is quite vast and that the remnant group of local Lorentz transformations includes one- and two-dimensional Abelian subgroups of the Lorentz group.
Nonequilibrium dynamical mean-field theory
NASA Astrophysics Data System (ADS)
Freericks, James
2007-03-01
Dynamical mean-field theory (DMFT) is establishing itself as one of the most powerful approaches to the quantum many-body problem in strongly correlated electron materials. Recently, the formalism has been generalized to study nonequilibrium problems [1,2], such as the evolution of Bloch oscillations in a material that changes from a diffusive metal to a Mott insulator [2,3]. Using a real-time formalism on the Kadanoff-Baym-Keldysh contour, the DMFT algorithm can be generalized to the case of systems that are not time-translation invariant. The computational algorithm has a parallel implementation with essentially a linear scale up when running on thousands of processors. Results on the decay of Bloch oscillations, their change of character within the Mott insulator, and movies on how electrons redistribute themselves due to their response to an external electrical field will be presented. In addition to solid-state applications, this work also applies to the behavior of mixtures of light and heavy cold atoms in optical lattices. [1] V. M. Turkowski and J. K. Freericks, Spectral moment sum rules for strongly correlated electrons in time-dependent electric fields, Phys. Rev. B 075108 (2006); Erratum, Phys. Rev. B 73, 209902(E) (2006). [2] J. K. Freericks, V. M. Turkowski , and V. Zlati'c, Nonlinear response of strongly correlated materials to large electric fields, in Proceedings of the HPCMP Users Group Conference 2006, Denver, CO, June 26--29, 2006 edited by D. E. Post (IEEE Computer Society, Los Alamitos, CA, 2006), to appear. [3] J. K. Freericks, V. M. Turkowski, and V. Zlati'c, Nonequilibrium dynamical mean-field theory, submitted to Phys. Rev. Lett. cond-mat//0607053.
An extremal ${\\mathcal{N}}=2$ superconformal field theory
Benjamin, Nathan; Dyer, Ethan; Fitzpatrick, A. Liam; Kachru, Shamit
2015-11-16
Here, we provide an example of an extremal chiral ${\\mathcal{N}}$ = 2 superconformal field theory at c = 24. The construction is based on a ${{\\mathbb{Z}}}_{2}$ orbifold of the theory associated to the ${A}_{1}^{24}$ Niemeier lattice. The statespace is governed by representations of the sporadic group M 23.
An extremal $${\\mathcal{N}}=2$$ superconformal field theory
Benjamin, Nathan; Dyer, Ethan; Fitzpatrick, A. Liam; Kachru, Shamit
2015-11-16
Here, we provide an example of an extremal chiralmore » $${\\mathcal{N}}$$ = 2 superconformal field theory at c = 24. The construction is based on a $${{\\mathbb{Z}}}_{2}$$ orbifold of the theory associated to the $${A}_{1}^{24}$$ Niemeier lattice. The statespace is governed by representations of the sporadic group M 23.« less
Renormalization group evolution of the universal theories EFT
Wells, James D.; Zhang, Zhengkang
2016-06-21
The conventional oblique parameters analyses of precision electroweak data can be consistently cast in the modern framework of the Standard Model effective field theory (SMEFT) when restrictions are imposed on the SMEFT parameter space so that it describes universal theories. However, the usefulness of such analyses is challenged by the fact that universal theories at the scale of new physics, where they are matched onto the SMEFT, can flow to nonuniversal theories with renormalization group (RG) evolution down to the electroweak scale, where precision observables are measured. The departure from universal theories at the electroweak scale is not arbitrary, butmore » dictated by the universal parameters at the matching scale. But to define oblique parameters, and more generally universal parameters at the electroweak scale that directly map onto observables, additional prescriptions are needed for the treatment of RG-induced nonuniversal effects. Finally, we perform a RG analysis of the SMEFT description of universal theories, and discuss the impact of RG on simplified, universal-theories-motivated approaches to fitting precision electroweak and Higgs data.« less
Introduction to conformal field theory and string theory
Dixon, L.J.
1989-12-01
These lectures are meant to provide a brief introduction to conformal field theory (CFT) and string theory for those with no prior exposure to the subjects. There are many excellent reviews already available, and most of these go in to much more detail than I will be able to here. 52 refs., 11 figs.
Fermion boson metamorphosis in field theory
Ha, Y.K.
1982-01-01
In two-dimensional field theories many features are especially transparent if the Fermi fields are represented by non-local expressions of the Bose fields. Such a procedure is known as boson representation. Bilinear quantities appear in the Lagrangian of a fermion theory transform, however, as simple local expressions of the bosons so that the resulting theory may be written as a theory of bosons. Conversely, a theory of bosons may be transformed into an equivalent theory of fermions. Together they provide a basis for generating many interesting equivalences between theories of different types. In the present work a consistent scheme for constructing a canonical Fermi field in terms of a real scalar field is developed and such a procedure is valid and consistent with the tenets of quantum field theory is verified. A boson formulation offers a unifying theme in understanding the structure of many theories. This is illustrated by the boson formulation of a multifermion theory with chiral and internal symmetries. The nature of dynamical generation of mass when the theory undergoes boson transmutation and the preservation of continuous chiral symmetry in the massive case are examined. The dynamics of the system depends to a great extent on the specific number of fermions and different models of the same system can have very different properties. Many unusual symmetries of the fermion theory, such as hidden symmetry, duality and triality symmetries, are only manifest in the boson formulation. The underlying connections between some models with U(N) internal symmetry and another class of fermion models built with Majorana fermions which have O(2N) internal symmetry are uncovered.
On causality in polymer scalar field theory
NASA Astrophysics Data System (ADS)
García-Chung, Angel A.; Morales-Técotl, Hugo A.
2011-10-01
The properties of spacetime corresponding to a proposed quantum gravity theory might modify the high energy behavior of quantum fields. Motivated by loop quantum gravity, recently, Hossain et al [1] have considered a polymer field algebra that replaces the standard canonical one in order to calculate the propagator of a real scalar field in flat spacetime. This propagator features Lorentz violations. Motivated by the relation between Lorentz invariance and causality in standard Quantum Field Theory, in this work we investigate the causality behavior of the polymer scalar field.
Supersymmetric N=2 gauge theory with arbitrary gauge group
NASA Astrophysics Data System (ADS)
Kuchiev, Michael Yu.
2010-10-01
A new universal model to implement the Seiberg-Witten approach to low-energy properties of the supersymmetric N=2 gauge theory with an arbitrary compact simple gauge group, classical or exceptional, is suggested. It is based on the hyperelliptic curve, whose genus equals the rank of the gauge group. The weak and strong coupling limits are reproduced. The magnetic and electric charges of light dyons, which are present in the proposed model comply with recent predictions derived from the general properties of the theory. The discrete chiral symmetry is implemented, the duality condition is reproduced, and connections between monodromies at weak and strong coupling are established. It is found that the spectra of monopoles and dyons are greatly simplified when vectors representing the scalar and dual fields in the Cartan algebra are aligned along the Weyl vector. This general feature of the theory is used for an additional verification of the model. The model predicts the identical analytic structures of the coupling constants for the theories based on the SU(r+1) and Sp(2r) gauge groups.
Three approaches to classical thermal field theory
Gozzi, E.; Penco, R.
2011-04-15
Research Highlights: > Classical thermal field theory admits three equivalent path integral formulations. > Classical Feynman rules can be derived for all three formulations. > Quantum Feynman rules reduce to classical ones at high temperatures. > Classical Feynman rules become much simpler when superfields are introduced. - Abstract: In this paper we study three different functional approaches to classical thermal field theory, which turn out to be the classical counterparts of three well-known different formulations of quantum thermal field theory: the closed-time path (CTP) formalism, the thermofield dynamics (TFD) and the Matsubara approach.
Renormalization group optimized perturbation theory at finite temperatures
NASA Astrophysics Data System (ADS)
Kneur, Jean-Loïc; Pinto, Marcus B.
2015-12-01
A recently developed variant of the so-called optimized perturbation theory (OPT), making it perturbatively consistent with renormalization group (RG) properties, RGOPT, was shown to drastically improve its convergence for zero temperature theories. Here the RGOPT adapted to finite temperature is illustrated with a detailed evaluation of the two-loop pressure for the thermal scalar λ ϕ4 field theory. We show that already at the simple one-loop level this quantity is exactly scale-invariant by construction and turns out to qualitatively reproduce, with a rather simple procedure, results from more sophisticated resummation methods at two-loop order, such as the two-particle irreducible approach typically. This lowest order also reproduces the exact large-N results of the O (N ) model. Although very close in spirit, our RGOPT method and corresponding results differ drastically from similar variational approaches, such as the screened perturbation theory or its QCD-version, the (resummed) hard thermal loop perturbation theory. The latter approaches exhibit a sensibly degrading scale dependence at higher orders, which we identify as a consequence of missing RG invariance. In contrast RGOPT gives a considerably reduced scale dependence at two-loop level, even for relatively large coupling values √{λ /24 }˜O (1 ), making results much more stable as compared with standard perturbation theory, with expected similar properties for thermal QCD.
Marginally Relevant Topics in Conformal Field Theories
NASA Astrophysics Data System (ADS)
Cleary, Kevin Francis
We consider a set of topics in conformal field theory. We provide an example of a 4D theory that exhibits the Contino-Pomarol-Rattazzi mechanism, where breaking conformal symmetry by an almost marginal operator leads to a light pseudo-Goldstone boson, the dilaton, and a parametrically suppressed contribution to vacuum energy. We consider SUSY QCD at the edge of the conformal window and break conformal symmetry by weakly gauging a subgroup of the flavor symmetry. Using Seiberg duality we show that for a range of parameters the singlet meson in the dual theory reaches the unitarity bound, however, this theory does not have a stable vacuum. We stabilize the vacuum with soft breaking terms, compute the mass of the dilaton, and determine the range of parameters where the leading contribution to the dilaton mass is from the almost marginal coupling. We also weigh in on a widely held belief that increasing bounds on the gluino mass, which feeds down to the stop mass through renormalization group running, are making a light stop increasingly unlikely. Here we present a counter-example. We examine the case of the Minimal Composite Supersymmetric Standard Model which has a light composite stop. The large anomalous dimension of the stop from strong dynamics pushes the stop mass toward a quasi-fixed point in the infrared, which is smaller than standard estimates by a factor of a large logarithm. The gluino can be about three times heavier than the stop, which is comparable to hierarchy achieved with supersoft Dirac gluino masses. Thus, in this class of models, a heavy gluino is not necessarily indicative of a heavy stop.
Ostrogradsky in theories with multiple fields
NASA Astrophysics Data System (ADS)
de Rham, Claudia; Matas, Andrew
2016-06-01
We review how the (absence of) Ostrogradsky instability manifests itself in theories with multiple fields. It has recently been appreciated that when multiple fields are present, the existence of higher derivatives may not automatically imply the existence of ghosts. We discuss the connection with gravitational theories like massive gravity and beyond Horndeski which manifest higher derivatives in some formulations and yet are free of Ostrogradsky ghost. We also examine an interesting new class of Extended Scalar-Tensor Theories of gravity which has been recently proposed. We show that for a subclass of these theories, the tensor modes are either not dynamical or are infinitely strongly coupled. Among the remaining theories for which the tensor modes are well-defined one counts one new model that is not field-redefinable to Horndeski via a conformal and disformal transformation but that does require the vacuum to break Lorentz invariance. We discuss the implications for the effective field theory of dark energy and the stability of the theory. In particular we find that if we restrict ourselves to the Extended Scalar-Tensor class of theories for which the tensors are well-behaved and the scalar is free from gradient or ghost instabilities on FLRW then we recover Horndeski up to field redefinitions.
3D quantum gravity and effective noncommutative quantum field theory.
Freidel, Laurent; Livine, Etera R
2006-06-01
We show that the effective dynamics of matter fields coupled to 3D quantum gravity is described after integration over the gravitational degrees of freedom by a braided noncommutative quantum field theory symmetric under a kappa deformation of the Poincaré group.
Metric quantum field theory: A preliminary look
Watson, W.N.
1988-01-01
Spacetime coordinates are involved in uncertainty relations; spacetime itself appears to exhibit curvature. Could the continua associated with field variables exhibit curvature This question, as well as the ideas that (a) difficulties with quantum theories of gravitation may be due to their formulation in an incorrect analogy with other quantum field theories, (b) spacetime variables should not be any more basic than others for describing physical phenomena, and (c) if field continua do not exhibit curvature, the reasons would be of interest, motivated the formulation of a theory of variable curvature and torsion in the electromagnetic four-potential's reciprocal space. Curvature and torsion equation completely analogous to those for a gauge theory of gravitation (the Einstein-Cartan-Sciama-Kibble theory) are assumed for this continuum. The interaction-Hamiltonian density of this theory, to a first approximation, implies that in addition to the Maxwell-Dirac field interaction of ordinary quantum electrodynamics, there should also be an interaction between Dirac-field vector and pseudovector currents unmediated by photons, as well as other interactions involving two or three Dirac-field currents interacting with the Maxwell field at single spacetime events. Calculations expressing Bhabha-scattering cross sections for incident beams with parallel spins differ from those of unmodified quantum electrodynamics by terms of first order in the gravitational constant of the theory, but the corresponding cross section for unpolarized incident beams differs from that of the unmodified theory only by terms of higher order in that constant. Undesirable features of the present theory include its nonrenormalizability, the obscurity of the meaning of its inverse field operator, and its being based on electrodynamics rather than electroweak dynamics.
Relativistic mean-field theory
NASA Astrophysics Data System (ADS)
Meng, Jie; Ring, Peter; Zhao, Pengwei
In this chapter, the covariant energy density functional is constructed with both the meson-exchange and the point-coupling pictures. Several widely used functionals with either nonlinear or density-dependent effective interactions are introduced. The applications of covariant density functional theory are demonstrated for infinite nuclear matter and finite nuclei with spherical symmetry, axially symmetric quadrupole deformation, and triaxial quadrupole shapes. Finally, a relativistic description of the nuclear landscape has been discussed, which is not only important for nuclear structure, but also important for nuclear astrophysics, where we are facing the problem of a reliable extrapolation to the very neutron-rich nuclei.
Better Field Instruction by Using Jigsaw Groups
NASA Astrophysics Data System (ADS)
Sammons, J. I.; Murray, D. P.
2006-12-01
Do any of these sound familiar? Most of my students do well at field stops, but there are always the few at the back. I'd like to guest speak at the local High School, but the students have too little background. I wish I could spark the interest of my introductory classes. Jigsaw is the solution to these problems. This easy-to-apply technique puts students in the driver's seat. They make the inferences-they own the discovery. You'll see that "A-ha!" as though it were a first time event. Jigsaw brings new excitement to familiar activities for every student in your class, even that guy in the back. Best of all, the technique does not depend on the style or force of personality of the instructor. It is easy to learn and suitable for use by Teaching Assistants. Here's how it works: 1. Identify the critical concepts necessary for a full understanding of the field stop or activity. 2. Divide your class into Expert Groups. The members of each Expert Group will master one of these critical concepts. 3.Dissolve the Expert Groups. Divide your class into new Jigsaw Groups to address the field stop or activity. Each Jigsaw Group includes members from each Expert Group. Like pieces of a puzzle, each Jigsaw Group member brings a critical piece to the problem. This talk will demonstrate Jigsaw Groups in action at a field stop. You'll see the crucial identification of critical concepts, small lab explorations carried out by the Expert Groups to master their assigned concepts, and Jigsaw Groups working a complex geological feature. You'll learn how to trouble-shoot less-than-successful first attempts and you'll leave with a step-by-step template that will allow you to adapt your existing activities to Jigsaw technique.
Pure field theories and MACSYMA algorithms
NASA Technical Reports Server (NTRS)
Ament, W. S.
1977-01-01
A pure field theory attempts to describe physical phenomena through singularity-free solutions of field equations resulting from an action principle. The physics goes into forming the action principle and interpreting specific results. Algorithms for the intervening mathematical steps are sketched. Vacuum general relativity is a pure field theory, serving as model and providing checks for generalizations. The fields of general relativity are the 10 components of a symmetric Riemannian metric tensor; those of the Einstein-Straus generalization are the 16 components of a nonsymmetric. Algebraic properties are exploited in top level MACSYMA commands toward performing some of the algorithms of that generalization. The light cone for the theory as left by Einstein and Straus is found and simplifications of that theory are discussed.
An action for F-theory: {SL}(2){{{R}}}^{+} exceptional field theory
NASA Astrophysics Data System (ADS)
Berman, David S.; Blair, Chris D. A.; Malek, Emanuel; Rudolph, Felix J.
2016-10-01
We construct the 12-dimensional exceptional field theory (EFT) associated to the group {SL}(2)× {{{R}}}+. Demanding the closure of the algebra of local symmetries leads to a constraint, known as the section condition, that must be imposed on all fields. This constraint has two inequivalent solutions, one giving rise to 11-dimensional supergravity and the other leading to F-theory. Thus {SL}(2)× {{{R}}}+ EFT contains both F-theory and M-theory in a single 12-dimensional formalism.
Pion masses in quasiconformal gauge field theories
Dietrich, Dennis D.; Jaervinen, Matti
2009-03-01
We study modifications to Weinberg-like sum rules in quasiconformal gauge field theories. Beyond the two Weinberg sum rules and the oblique S parameter, we study the pion mass and the X parameter. Especially, we evaluate the pion mass for walking technicolor theories, in particular, minimal walking technicolor, and find contributions of the order of up to several hundred GeV.
Reductionism, emergence, and effective field theories
NASA Astrophysics Data System (ADS)
Castellani, Elena
In recent years, a "change in attitude" in particle physics has led to our understanding current quantum field theories as effective field theories (EFTs). The present paper is concerned with the significance of this EFT approach, especially from the viewpoint of the debate on reductionism in science. In particular, I shall show how EFTs provide a new and interesting case study in current philosophical discussion on reduction, emergence, and inter-level relationships in general.
Geometric continuum regularization of quantum field theory
Halpern, M.B. . Dept. of Physics)
1989-11-08
An overview of the continuum regularization program is given. The program is traced from its roots in stochastic quantization, with emphasis on the examples of regularized gauge theory, the regularized general nonlinear sigma model and regularized quantum gravity. In its coordinate-invariant form, the regularization is seen as entirely geometric: only the supermetric on field deformations is regularized, and the prescription provides universal nonperturbative invariant continuum regularization across all quantum field theory. 54 refs.
{N}=3 four dimensional field theories
NASA Astrophysics Data System (ADS)
García-Etxebarria, Iñaki; Regalado, Diego
2016-03-01
We introduce a class of four dimensional field theories constructed by quotienting ordinary {N}=4 U(N ) SYM by particular combinations of R-symmetry and SL(2, ℤ) automorphisms. These theories appear naturally on the worldvolume of D3 branes probing terminal singularities in F-theory, where they can be thought of as non-perturbative generalizations of the O3 plane. We focus on cases preserving only 12 supercharges, where the quotient gives rise to theories with coupling fixed at a value of order one. These constructions possess an unconventional large N limit described by a non-trivial F-theory fibration with base AdS 5 × (S 5/ ℤ k ). Upon reduction on a circle the {N}=3 theories flow to well-known {N}=6 ABJM theories.
Holographic renormalization group and cosmology in theories with quasilocalized gravity
NASA Astrophysics Data System (ADS)
Csáki, Csaba; Erlich, Joshua; Hollowood, Timothy J.; Terning, John
2001-03-01
We study the long distance behavior of brane theories with quasilocalized gravity. The five-dimensional (5D) effective theory at large scales follows from a holographic renormalization group flow. As intuitively expected, the graviton is effectively four dimensional at intermediate scales and becomes five dimensional at large scales. However, in the holographic effective theory the essentially 4D radion dominates at long distances and gives rise to scalar antigravity. The holographic description shows that at large distances the Gregory-Rubakov-Sibiryakov (GRS) model is equivalent to the model recently proposed by Dvali, Gabadadze, and Porrati (DGP), where a tensionless brane is embedded into 5D Minkowski space, with an additional induced 4D Einstein-Hilbert term on the brane. In the holographic description the radion of the GRS model is automatically localized on the tensionless brane, and provides the ghostlike field necessary to cancel the extra graviton polarization of the DGP model. Thus, there is a holographic duality between these theories. This analysis provides physical insight into how the GRS model works at intermediate scales; in particular it sheds light on the size of the width of the graviton resonance, and also demonstrates how the holographic renormalization group can be used as a practical tool for calculations.
THE VELOCITY FIELD AROUND GROUPS OF GALAXIES
Hartwick, F. D. A.
2011-06-15
A statistical method is presented for determining the velocity field in the immediate vicinity of groups of galaxies using only positional and redshift information with the goal of studying the perturbation of the Hubble flow around groups more distant than the Local Group. The velocities are assumed to obey a Hubble-like expansion law, i.e., V = H{sub exp} R, where the expansion rate H{sub exp} is to be determined. The method is applied to a large, representative group catalog and evidence is found for a sub-Hubble expansion rate within two well-defined radii beyond the virial radii of the groups. This result is consistent with that of Teerikorpi et al. who found a similar expansion law around three nearby groups and extends it to a more representative volume of space.
The Local Group: the ultimate deep field
NASA Astrophysics Data System (ADS)
Boylan-Kolchin, Michael; Weisz, Daniel R.; Bullock, James S.; Cooper, Michael C.
2016-10-01
Near-field cosmology - using detailed observations of the Local Group and its environs to study wide-ranging questions in galaxy formation and dark matter physics - has become a mature and rich field over the past decade. There are lingering concerns, however, that the relatively small size of the present-day Local Group (˜2 Mpc diameter) imposes insurmountable sample-variance uncertainties, limiting its broader utility. We consider the region spanned by the Local Group's progenitors at earlier times and show that it reaches 3 arcmin ≈ 7 comoving Mpc in linear size (a volume of ≈350 Mpc3) at z = 7. This size at early cosmic epochs is large enough to be representative in terms of the matter density and counts of dark matter haloes with Mvir(z = 7) ≲ 2 × 109 M⊙. The Local Group's stellar fossil record traces the cosmic evolution of galaxies with 103 ≲ M⋆(z = 0)/M⊙ ≲ 109 (reaching M1500 > -9 at z ˜ 7) over a region that is comparable to or larger than the Hubble Ultra-Deep Field (HUDF) for the entire history of the Universe. In the JWST era, resolved stellar populations will probe regions larger than the HUDF and any deep JWST fields, further enhancing the value of near-field cosmology.
Far-field environment working group summary
Pearcy, E.C.; Cady, R.E.
1995-09-01
This article is a summary of the proceedings of a group discussion which took place at the Workshop on the Role of Natural Analogs in Geologic Disposal of High-Level Nuclear Waste in San Antonio, Texas on July 22-25, 1991. The working group concentrated on the subject of the potential impacts of underground disposal of high-level radioactive wastes on the far-field environment.
"Quantum Field Theory and QCD"
Jaffe, Arthur M.
2006-02-25
This grant partially funded a meeting, "QFT & QCD: Past, Present and Future" held at Harvard University, Cambridge, MA on March 18-19, 2005. The participants ranged from senior scientists (including at least 9 Nobel Prize winners, and 1 Fields medalist) to graduate students and undergraduates. There were several hundred persons in attendance at each lecture. The lectures ranged from superlative reviews of past progress, lists of important, unsolved questions, to provocative hypotheses for future discovery. The project generated a great deal of interest on the internet, raising awareness and interest in the open questions of theoretical physics.
Quantum algorithms for quantum field theories.
Jordan, Stephen P; Lee, Keith S M; Preskill, John
2012-06-01
Quantum field theory reconciles quantum mechanics and special relativity, and plays a central role in many areas of physics. We developed a quantum algorithm to compute relativistic scattering probabilities in a massive quantum field theory with quartic self-interactions (φ(4) theory) in spacetime of four and fewer dimensions. Its run time is polynomial in the number of particles, their energy, and the desired precision, and applies at both weak and strong coupling. In the strong-coupling and high-precision regimes, our quantum algorithm achieves exponential speedup over the fastest known classical algorithm. PMID:22654052
Quantum algorithms for quantum field theories.
Jordan, Stephen P; Lee, Keith S M; Preskill, John
2012-06-01
Quantum field theory reconciles quantum mechanics and special relativity, and plays a central role in many areas of physics. We developed a quantum algorithm to compute relativistic scattering probabilities in a massive quantum field theory with quartic self-interactions (φ(4) theory) in spacetime of four and fewer dimensions. Its run time is polynomial in the number of particles, their energy, and the desired precision, and applies at both weak and strong coupling. In the strong-coupling and high-precision regimes, our quantum algorithm achieves exponential speedup over the fastest known classical algorithm.
The Theory of Quantized Fields. II
DOE R&D Accomplishments Database
Schwinger, J.
1951-01-01
The arguments leading to the formulation of the Action Principle for a general field are presented. In association with the complete reduction of all numerical matrices into symmetrical and anti-symmetrical parts, the general field is decomposed into two sets, which are identified with Bose-Einstein and Fermi-Dirac fields. The spin restriction on the two kinds of fields is inferred from the time reflection invariance requirement. The consistency of the theory is verified in terms of a criterion involving the various generators of infinitesimal transformations. Following a discussion of charged fields, the electromagnetic field is introduced to satisfy the postulate of general gauge invariance. As an aspect of the latter, it is recognized that the electromagnetic field and charged fields are not kinematically independent. After a discussion of the field-strength commutation relations, the independent dynamical variable of the electromagnetic field are exhibited in terms of a special gauge.
Equilibration properties of classical integrable field theories
NASA Astrophysics Data System (ADS)
De Luca, Andrea; Mussardo, Giuseppe
2016-06-01
We study the equilibration properties of classical integrable field theories at a finite energy density, with a time evolution that starts from initial conditions far from equilibrium. These classical field theories may be regarded as quantum field theories in the regime of high occupation numbers. This observation permits to recover the classical quantities from the quantum ones by taking a proper \\hslash \\to 0 limit. In particular, the time averages of the classical theories can be expressed in terms of a suitable version of the LeClair-Mussardo formula relative to the generalized Gibbs ensemble. For the purposes of handling time averages, our approach provides a solution of the problem of the infinite gap solutions of the inverse scattering method.
Attachment to groups: theory and measurement.
Smith, E R; Murphy, J; Coats, S
1999-07-01
Aspects of people's identification with groups may be understood by borrowing theoretical ideas and measurement strategies from research on attachment in close relationships. People have mental models of the self as a group member and of groups as sources of identity and esteem. These models affect thoughts, emotions, and behaviors related to group membership. Three studies show that two dimensions of attachment to groups, attachment anxiety and avoidance, can be assessed with good reliability, validity, and over-time stability. These factors are distinct from relationship attachment and from other measures of group identification. Group attachment predicts several important outcomes, including emotions concerning the group, time and activities shared with a group, social support, collective self-esteem, and ways of resolving conflict. This conceptualization provides new insights into the nature of people's psychological ties to groups.
From theory to field experiments
NASA Astrophysics Data System (ADS)
de Vos, Bram
2016-04-01
Peter Raats' achievements in Haren (NL) 1986-1997 were based on a solid theoretical insight in hydrology and transport process in soil. However, Peter was also the driving force behind many experimental studies and applied research. This will be illustrated by a broad range of examples ranging from the dynamics of composting processes of organic material; modelling and monitoring nutrient leaching at field-scale; wind erosion; water and nutrient dynamics in horticultural production systems; oxygen diffusion in soils; and processes of water and nutrient uptake by plant roots. Peter's leadership led to may new approaches and the introduction of innovative measurement techniques in Dutch research; ranging from TDR to nutrient concentration measurements in closed fertigation systems. This presentation will give a brief overview how Peter's theoretical and mathematical insights accelerated this applied research.
Hunton Group core workshop and field trip
Johnson, K.S.
1993-12-31
The Late Ordovician-Silurian-Devonian Hunton Group is a moderately thick sequence of shallow-marine carbonates deposited on the south edge of the North American craton. This rock unit is a major target for petroleum exploration and reservoir development in the southern Midcontinent. The workshop described here was held to display cores, outcrop samples, and other reservoir-characterization studies of the Hunton Group and equivalent strata throughout the region. A field trip was organized to complement the workshop by allowing examination of excellent outcrops of the Hunton Group of the Arbuckle Mountains.
New symbolic tools for differential geometry, gravitation, and field theory
NASA Astrophysics Data System (ADS)
Anderson, I. M.; Torre, C. G.
2012-01-01
DifferentialGeometry is a Maple software package which symbolically performs fundamental operations of calculus on manifolds, differential geometry, tensor calculus, spinor calculus, Lie algebras, Lie groups, transformation groups, jet spaces, and the variational calculus. These capabilities, combined with dramatic recent improvements in symbolic approaches to solving algebraic and differential equations, have allowed for development of powerful new tools for solving research problems in gravitation and field theory. The purpose of this paper is to describe some of these new tools and present some advanced applications involving: Killing vector fields and isometry groups, Killing tensors, algebraic classification of solutions of the Einstein equations, and symmetry reduction of field equations.
Phase-space quantization of field theory.
Curtright, T.; Zachos, C.
1999-04-20
In this lecture, a limited introduction of gauge invariance in phase-space is provided, predicated on canonical transformations in quantum phase-space. Exact characteristic trajectories are also specified for the time-propagating Wigner phase-space distribution function: they are especially simple--indeed, classical--for the quantized simple harmonic oscillator. This serves as the underpinning of the field theoretic Wigner functional formulation introduced. Scalar field theory is thus reformulated in terms of distributions in field phase-space. This is a pedagogical selection from work published and reported at the Yukawa Institute Workshop ''Gauge Theory and Integrable Models'', 26-29 January, 1999.
Generalized metric formulation of double field theory
NASA Astrophysics Data System (ADS)
Hohm, Olaf; Hull, Chris; Zwiebach, Barton
2010-08-01
The generalized metric is a T-duality covariant symmetric matrix constructed from the metric and two-form gauge field and arises in generalized geometry. We view it here as a metric on the doubled spacetime and use it to give a simple formulation with manifest T-duality of the double field theory that describes the massless sector of closed strings. The gauge transformations are written in terms of a generalized Lie derivative whose commutator algebra is defined by a double field theory extension of the Courant bracket.
Protected gates for topological quantum field theories
NASA Astrophysics Data System (ADS)
Beverland, Michael E.; Buerschaper, Oliver; Koenig, Robert; Pastawski, Fernando; Preskill, John; Sijher, Sumit
2016-02-01
We study restrictions on locality-preserving unitary logical gates for topological quantum codes in two spatial dimensions. A locality-preserving operation is one which maps local operators to local operators — for example, a constant-depth quantum circuit of geometrically local gates, or evolution for a constant time governed by a geometrically local bounded-strength Hamiltonian. Locality-preserving logical gates of topological codes are intrinsically fault tolerant because spatially localized errors remain localized, and hence sufficiently dilute errors remain correctable. By invoking general properties of two-dimensional topological field theories, we find that the locality-preserving logical gates are severely limited for codes which admit non-abelian anyons, in particular, there are no locality-preserving logical gates on the torus or the sphere with M punctures if the braiding of anyons is computationally universal. Furthermore, for Ising anyons on the M-punctured sphere, locality-preserving gates must be elements of the logical Pauli group. We derive these results by relating logical gates of a topological code to automorphisms of the Verlinde algebra of the corresponding anyon model, and by requiring the logical gates to be compatible with basis changes in the logical Hilbert space arising from local F-moves and the mapping class group.
Small Group Learning: Do Group Members' Implicit Theories of Ability Make a Difference?
ERIC Educational Resources Information Center
Beckmann, Nadin; Wood, Robert E.; Minbashian, Amirali; Tabernero, Carmen
2012-01-01
We examined the impact of members' implicit theories of ability on group learning and the mediating role of several group process variables, such as goal-setting, effort attributions, and efficacy beliefs. Comparisons were between 15 groups with a strong incremental view on ability (high incremental theory groups), and 15 groups with a weak…
Parafermionic conformal field theory on the lattice
NASA Astrophysics Data System (ADS)
Mong, Roger S. K.; Clarke, David J.; Alicea, Jason; Lindner, Netanel H.; Fendley, Paul
2014-11-01
Finding the precise correspondence between lattice operators and the continuum fields that describe their long-distance properties is a largely open problem for strongly interacting critical points. Here, we solve this problem essentially completely in the case of the three-state Potts model, which exhibits a phase transition described by a strongly interacting ‘parafermion’ conformal field theory. Using symmetry arguments, insights from integrability, and extensive simulations, we construct lattice analogues of nearly all the relevant and marginal physical fields governing this transition. This construction includes chiral fields such as the parafermion. Along the way we also clarify the structure of operator product expansions between order and disorder fields, which we confirm numerically. Our results both suggest a systematic methodology for attacking non-free field theories on the lattice and find broader applications in the pursuit of exotic topologically ordered phases of matter.
Bound states in gauge theories as the Poincare group representations
Cherny, A. Yu.; Dorokhov, A. E.; Han, Nguyen Suan; Pervushin, V. N. Shilin, V. I.
2013-03-15
The bound-state generating functional is constructed in gauge theories. This construction is based on the Dirac Hamiltonian approach to gauge theories, the Poincare group classification of fields and their nonlocal bound states, and the Markov-Yukawa constraint of irreducibility. The generating functional contains additional anomalous creations of pseudoscalar bound states: para-positronium in QED and mesons inQCDin the two-gamma processes of the type of {gamma} + {gamma} {yields} {pi}{sub 0} +para-positronium. The functional allows us to establish physically clear and transparent relations between the perturbativeQCD to its nonperturbative low-energy model by means of normal ordering and the quark and gluon condensates. In the limit of small current quark masses, the Gell-Mann-Oakes-Renner relation is derived from the Schwinger-Dyson and Bethe-Salpeter equations. The constituent quark masses can be calculated from a self-consistent nonlinear equation.
Free Quantum Field Theory from Quantum Cellular Automata
NASA Astrophysics Data System (ADS)
Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo; Tosini, Alessandro
2015-10-01
After leading to a new axiomatic derivation of quantum theory (see D'Ariano et al. in Found Phys, 2015), the new informational paradigm is entering the domain of quantum field theory, suggesting a quantum automata framework that can be regarded as an extension of quantum field theory to including an hypothetical Planck scale, and with the usual quantum field theory recovered in the relativistic limit of small wave-vectors. Being derived from simple principles (linearity, unitarity, locality, homogeneity, isotropy, and minimality of dimension), the automata theory is quantum ab-initio, and does not assume Lorentz covariance and mechanical notions. Being discrete it can describe localized states and measurements (unmanageable by quantum field theory), solving all the issues plaguing field theory originated from the continuum. These features make the theory an ideal framework for quantum gravity, with relativistic covariance and space-time emergent solely from the interactions, and not assumed a priori. The paper presents a synthetic derivation of the automata theory, showing how the principles lead to a description in terms of a quantum automaton over a Cayley graph of a group. Restricting to Abelian groups we show how the automata recover the Weyl, Dirac and Maxwell dynamics in the relativistic limit. We conclude with some new routes about the more general scenario of non-Abelian Cayley graphs. The phenomenology arising from the automata theory in the ultra-relativistic domain and the analysis of corresponding distorted Lorentz covariance is reviewed in Bisio et al. (Found Phys 2015, in this same issue).
Cutkosky rules for superstring field theory
NASA Astrophysics Data System (ADS)
Pius, Roji; Sen, Ashoke
2016-10-01
Superstring field theory expresses the perturbative S-matrix of superstring theory as a sum of Feynman diagrams each of which is manifestly free from ultraviolet divergences. The interaction vertices fall off exponentially for large space-like external momenta making the ultraviolet finiteness property manifest, but blow up exponentially for large time-like external momenta making it impossible to take the integration contours for loop energies to lie along the real axis. This forces us to carry out the integrals over the loop energies by choosing appropriate contours in the complex plane whose ends go to infinity along the imaginary axis but which take complicated form in the interior navigating around the various poles of the propagators. We consider the general class of quantum field theories with this property and prove Cutkosky rules for the amplitudes to all orders in perturbation theory. Besides having applications to string field theory, these results also give an alternative derivation of Cutkosky rules in ordinary quantum field theories.
Effective Field Theories, Reductionism and Scientific Explanation
NASA Astrophysics Data System (ADS)
Hartmann, Stephan
Effective field theories have been a very popular tool in quantum physics for almost two decades. And there are good reasons for this. I will argue that effective field theories share many of the advantages of both fundamental theories and phenomenological models, while avoiding their respective shortcomings. They are, for example, flexible enough to cover a wide range of phenomena, and concrete enough to provide a detailed story of the specific mechanisms at work at a given energy scale. So will all of physics eventually converge on effective field theories? This paper argues that good scientific research can be characterised by a fruitful interaction between fundamental theories, phenomenological models and effective field theories. All of them have their appropriate functions in the research process, and all of them are indispensable. They complement each other and hang together in a coherent way which I shall characterise in some detail. To illustrate all this I will present a case study from nuclear and particle physics. The resulting view about scientific theorising is inherently pluralistic, and has implications for the debates about reductionism and scientific explanation.
Effective Group Dynamics: Theories and Practices.
ERIC Educational Resources Information Center
Murk, Peter J.
Using a brief experiential group activity called "Choosing a Color Exercise" as an introductory measure, this paper explains the basics of group dynamics and reviews the major theoretical relationships between the group's structure, the dynamics of maintenance and task behaviors, and effective individual performances. The types of functional and…
Nonequilibrium statistical field theory for classical particles: Basic kinetic theory.
Viermann, Celia; Fabis, Felix; Kozlikin, Elena; Lilow, Robert; Bartelmann, Matthias
2015-06-01
Recently Mazenko and Das and Mazenko [Phys. Rev. E 81, 061102 (2010); J. Stat. Phys. 149, 643 (2012); J. Stat. Phys. 152, 159 (2013); Phys. Rev. E 83, 041125 (2011)] introduced a nonequilibrium field-theoretical approach to describe the statistical properties of a classical particle ensemble starting from the microscopic equations of motion of each individual particle. We use this theory to investigate the transition from those microscopic degrees of freedom to the evolution equations of the macroscopic observables of the ensemble. For the free theory, we recover the continuity and Jeans equations of a collisionless gas. For a theory containing two-particle interactions in a canonical perturbation series, we find the macroscopic evolution equations to be described by the Born-Bogoliubov-Green-Kirkwood-Yvon hierarchy with a truncation criterion depending on the order in perturbation theory. This establishes a direct link between the classical and the field-theoretical approaches to kinetic theory that might serve as a starting point to investigate kinetic theory beyond the classical limits.
Working group on chromospheric fields - Canopies
NASA Technical Reports Server (NTRS)
Jones, H. P.
1985-01-01
Although there are many points of uncertainty and controversy, the working group on chromospheric fields focussed its discussion on the concept of canopies; i.e., no one disagreed that a central issue relating to magnetic fields and chromospheric models is to learn how the photospheric field spreads with height. However, it quickly became apparent that in the time available, there was little prospect of building new unified models of magnetic field phenomena in the chromosphere beyond the scope of the formal presentations. Thus, the discussion was devoted to formulating questions which seemed both possible to address in future work and important for advancing understanding of the chromosphere. It began by discussing unresolved physical issues (almost everything) and then proceeded to consider means, both observational and synthetic, to address them.
Dynamical theory of dense groups of galaxies
NASA Technical Reports Server (NTRS)
Mamon, Gary A.
1990-01-01
It is well known that galaxies associate in groups and clusters. Perhaps 40% of all galaxies are found in groups of 4 to 20 galaxies (e.g., Tully 1987). Although most groups appear to be so loose that the galaxy interactions within them ought to be insignificant, the apparently densest groups, known as compact groups appear so dense when seen in projection onto the plane of the sky that their members often overlap. These groups thus appear as dense as the cores of rich clusters. The most popular catalog of compact groups, compiled by Hickson (1982), includes isolation among its selection critera. Therefore, in comparison with the cores of rich clusters, Hickson's compact groups (HCGs) appear to be the densest isolated regions in the Universe (in galaxies per unit volume), and thus provide in principle a clean laboratory for studying the competition of very strong gravitational interactions. The $64,000 question here is then: Are compact groups really bound systems as dense as they appear? If dense groups indeed exist, then one expects that each of the dynamical processes leading to the interaction of their member galaxies should be greatly enhanced. This leads us to the questions: How stable are dense groups? How do they form? And the related question, fascinating to any theorist: What dynamical processes predominate in dense groups of galaxies? If HCGs are not bound dense systems, but instead 1D change alignments (Mamon 1986, 1987; Walke & Mamon 1989) or 3D transient cores (Rose 1979) within larger looser systems of galaxies, then the relevant question is: How frequent are chance configurations within loose groups? Here, the author answers these last four questions after comparing in some detail the methods used and the results obtained in the different studies of dense groups.
Field Theory for Multi-Particle System
NASA Astrophysics Data System (ADS)
Wang, Shouhong; Ma, Tian
2016-03-01
The main objectives of this talk are 1) to introduce some basic postulates for quantum multi-particle systems, and 2) to develop a universal field theory for interacting multi-particle systems coupling both particle fields and interacting fields. By carefully examining the nature of interactions between multi-particles, we conclude that multi-particle systems must obey i) the gauge symmetry, ii) the principle of interaction dynamics (PID), and iii) the principle of representation invariance (PRI). Intuitively, PID takes the variation of the action functional under energy-momentum conservation constraint, offers a different and natural way of introducing Higgs fields, and is also required by the presence of dark matter and dark energy and the quark confinement. PRI requires that the SU(N) gauge theory be independent of representations of SU(N). Based on these principles, a few basic postulates for multi-particle systems are introduced in this talk, leading to a field theory for interacting multi-particle systems. A direct consequence of the field theory is the derivation of general atomic spectrum equations. Supported in Part by the Office of Naval Research, by the US National Science Foundation, and by the Chinese National Science Foundation.
Caustic Formation in Tachyon Effective Field Theories
NASA Astrophysics Data System (ADS)
Barnaby, Neil
2004-07-01
Certain configurations of D-branes, for example wrong dimensional branes or the brane-antibrane system, are unstable to decay. This instability is described by the appearance of a tachyonic mode in the spectrum of open strings ending on the brane(s). The decay of these unstable systems is described by the rolling of the tachyon field from the unstable maximum to the minimum of its potential. We analytically study the dynamics of the inhomogeneous tachyon field as it rolls towards the true vacuum of the theory in the context of several different tachyon effective actions. We find that the vacuum dynamics of these theories is remarkably similar and in particular we show that in all cases the tachyon field forms caustics where second and higher derivatives of the field blow up. The formation of caustics signals a pathology in the evolution since each of the effective actions considered is not reliable in the vicinity of a caustic. We speculate that the formation of caustics is an artifact of truncating the tachyon action, which should contain all orders of derivatives acting on the field, to a finite number of derivatives. Finally, we consider inhomogeneous solutions in p-adic string theory, a toy model of the bosonic tachyon which contains derivatives of all orders acting on the field. For a large class of initial conditions we conclusively show that the evolution is well behaved in this case. It is unclear if these caustics are a genuine prediction of string theory or not.
The amplitude of quantum field theory
Medvedev, B.V. ); Pavlov, V.P.; Polivanov, M.K. ); Sukhanov, A.D. )
1989-05-01
General properties of the transition amplitude in axiomatic quantum field theory are discussed. Bogolyubov's axiomatic method is chosen as the variant of the theory. The axioms of this method are analyzed. In particular, the significance of the off-shell extension and of the various forms of the causality condition are examined. A complete proof is given of the existence of a single analytic function whose boundary values are the amplitudes of all channels of a process with given particle number.
Magnetic monopoles in field theory and cosmology.
Rajantie, Arttu
2012-12-28
The existence of magnetic monopoles is predicted by many theories of particle physics beyond the standard model. However, in spite of extensive searches, there is no experimental or observational sign of them. I review the role of magnetic monopoles in quantum field theory and discuss their implications for particle physics and cosmology. I also highlight their differences and similarities with monopoles found in frustrated magnetic systems.
Supergeometry in Locally Covariant Quantum Field Theory
NASA Astrophysics Data System (ADS)
Hack, Thomas-Paul; Hanisch, Florian; Schenkel, Alexander
2016-03-01
In this paper we analyze supergeometric locally covariant quantum field theories. We develop suitable categories SLoc of super-Cartan supermanifolds, which generalize Lorentz manifolds in ordinary quantum field theory, and show that, starting from a few representation theoretic and geometric data, one can construct a functor A : SLoc to S* Alg to the category of super-*-algebras, which can be interpreted as a non-interacting super-quantum field theory. This construction turns out to disregard supersymmetry transformations as the morphism sets in the above categories are too small. We then solve this problem by using techniques from enriched category theory, which allows us to replace the morphism sets by suitable morphism supersets that contain supersymmetry transformations as their higher superpoints. We construct super-quantum field theories in terms of enriched functors eA : eSLoc to eS* Alg between the enriched categories and show that supersymmetry transformations are appropriately described within the enriched framework. As examples we analyze the superparticle in 1|1-dimensions and the free Wess-Zumino model in 3|2-dimensions.
The field theory of specific heat
NASA Astrophysics Data System (ADS)
Gusev, Yu. V.
2016-01-01
Finite temperature quantum field theory in the heat kernel method is used to study the heat capacity of condensed matter. The lattice heat is treated à la P. Debye as energy of the elastic (sound) waves. The dimensionless functional of free energy is re-derived with a cut-off parameter and used to obtain the specific heat of crystal lattices. The new dimensionless thermodynamical variable is formed as Planck's inverse temperature divided by the lattice constant. The dimensionless constant, universal for the class of crystal lattices, which determines the low temperature region of molar specific heat, is introduced and tested with the data for diamond lattice crystals. The low temperature asymptotics of specific heat is found to be the fourth power in temperature instead of the cubic power law of the Debye theory. Experimental data for the carbon group elements (silicon, germanium) and other materials decisively confirm the quartic law. The true low temperature regime of specific heat is defined by the surface heat, therefore, it depends on the geometrical characteristics of the body, while the absolute zero temperature limit is geometrically forbidden. The limit on the growth of specific heat at temperatures close to critical points, known as the Dulong-Petit law, appears from the lattice constant cut-off. Its value depends on the lattice type and it is the same for materials with the same crystal lattice. The Dulong-Petit values of compounds are equal to those of elements with the same crystal lattice type, if one mole of solid state matter were taken as the Avogadro number of the composing atoms. Thus, the Neumann-Kopp law is valid only in some special cases.
Electroweak Sudakov Corrections using Effective Field Theory
Chiu Juiyu; Golf, Frank; Kelley, Randall; Manohar, Aneesh V.
2008-01-18
Electroweak Sudakov corrections of the form {alpha}{sup n}log{sup m}s/M{sub W,Z}{sup 2} are summed using renormalization group evolution in soft-collinear effective theory. Results are given for the scalar, vector, and tensor form factors for fermion and scalar particles. The formalism for including massive gauge bosons in soft-collinear effective theory is developed.
Effective field theory for deformed atomic nuclei
NASA Astrophysics Data System (ADS)
Papenbrock, T.; Weidenmüller, H. A.
2016-05-01
We present an effective field theory (EFT) for a model-independent description of deformed atomic nuclei. In leading order this approach recovers the well-known results from the collective model by Bohr and Mottelson. When higher-order corrections are computed, the EFT accounts for finer details such as the variation of the moment of inertia with the band head and the small magnitudes of interband E2 transitions. For rotational bands with a finite spin of the band head, the EFT is equivalent to the theory of a charged particle on the sphere subject to a magnetic monopole field.
Dual field theory of strong interactions
Akers, D.
1987-07-01
A dual field theory of strong interactions is derived from a Lagrangian of the Yang-Mills and Higgs fields. The existence of a magnetic monopole of mass 2397 MeV and Dirac charge g = (137/2)e is incorporated into the theory. Unification of the strong, weak, and electromagnetic forces is shown to converge at the mass of the intermediate vector boson W/sup +/-/. The coupling constants of the strong and weak interactions are derived in terms of the fine-structure constant ..cap alpha.. = 1/137.
Effective field theory for deformed atomic nuclei
Papenbrock, Thomas F.; Weidenmüller, H. A.
2016-04-13
In this paper, we present an effective field theory (EFT) for a model-independent description of deformed atomic nuclei. In leading order this approach recovers the well-known results from the collective model by Bohr and Mottelson. When higher-order corrections are computed, the EFT accounts for finer details such as the variation of the moment of inertia with the band head and the small magnitudes of interband E2 transitions. Finally, for rotational bands with a finite spin of the band head, the EFT is equivalent to the theory of a charged particle on the sphere subject to a magnetic monopole field.
Long-range interactions in lattice field theory
Rabin, J.M.
1981-06-01
Lattice quantum field theories containing fermions can be formulated in a chirally invariant way provided long-range interactions are introduced. It is established that in weak-coupling perturbation theory such a lattice theory is renormalizable when the corresponding continuum theory is, and that the continuum theory is indeed recovered in the perturbative continuum limit. In the strong-coupling limit of these theories one is led to study an effective Hamiltonian describing a Heisenberg antiferromagnet with long-range interactions. Block-spin renormalization group methods are used to find a critical rate of falloff of the interactions, approximately as inverse distance squared, which separates a nearest-neighbor-antiferromagnetic phase from a phase displaying identifiable long-range effects. A duality-type symmetry is present in some block-spin calculations.
Natural discretization in noncommutative field theory
Acatrinei, Ciprian Sorin
2015-12-07
A discretization scheme for field theory is developed, in which the space time coordinates are assumed to be operators forming a noncommutative algebra. Generic waves without rotational symmetry are studied in (2+1) - dimensional scalar field theory with Heisenberg-type noncommutativity. In the representation chosen, the radial coordinate is naturally rendered discrete. Nonlocality along this coordinate, induced by noncommutativity, accounts for the angular dependence of the fields. A complete solution and the interpretation of its nonlocal features are given. The exact form of standing and propagating waves on such a discrete space is found in terms of finite series. A precise correspondence is established between the degree of nonlocality and the angular momentum of a field configuration. At small distance no classical singularities appear, even at the location of the sources. At large radius one recovers the usual commutative/continuum behaviour.
Astrophysical data analysis with information field theory
Enßlin, Torsten
2014-12-05
Non-parametric imaging and data analysis in astrophysics and cosmology can be addressed by information field theory (IFT), a means of Bayesian, data based inference on spatially distributed signal fields. IFT is a statistical field theory, which permits the construction of optimal signal recovery algorithms. It exploits spatial correlations of the signal fields even for nonlinear and non-Gaussian signal inference problems. The alleviation of a perception threshold for recovering signals of unknown correlation structure by using IFT will be discussed in particular as well as a novel improvement on instrumental self-calibration schemes. IFT can be applied to many areas. Here, applications in in cosmology (cosmic microwave background, large-scale structure) and astrophysics (galactic magnetism, radio interferometry) are presented.
Generalized Quantum Theory and Mathematical Foundations of Quantum Field Theory
NASA Astrophysics Data System (ADS)
Maroun, Michael Anthony
This dissertation is divided into two main topics. The first is the generalization of quantum dynamics when the Schrodinger partial differential equation is not defined even in the weak mathematical sense because the potential function itself is a distribution in the spatial variable, the same variable that is used to define the kinetic energy operator, i.e. the Laplace operator. The procedure is an extension and broadening of the distributional calculus and offers spectral results as an alternative to the only other two known methods to date, namely a) the functional calculi; and b) non-standard analysis. Furthermore, the generalizations of quantum dynamics presented within give a resolution to the time asymmetry paradox created by multi-particle quantum mechanics due to the time evolution still being unitary. A consequence is the randomization of phases needed for the fundamental justification Pauli master equation. The second topic is foundations of the quantum theory of fields. The title is phrased as ``foundations'' to emphasize that there is no claim of uniqueness but rather a proposal is put forth, which is markedly different than that of constructive or axiomatic field theory. In particular, the space of fields is defined as a space of generalized functions with involutive symmetry maps (the CPT invariance) that affect the topology of the field space. The space of quantum fields is then endowed the Frechet property and interactions change the topology in such a way as to cause some field spaces to be incompatible with others. This is seen in the consequences of the Haag theorem. Various examples and discussions are given that elucidate a new view of the quantum theory of fields and its (lack of) mathematical structure.
Not Available
1992-01-01
The effort of the experimental group has been concentrated on the CERN ALEPH and FERMILAB D0 collider experiments and completion of two fixed target experiments. The BNL fixed target experiment 771 took the world's largest sample of D(1285) and E/iota(1420) events, using pion, kaon and antiproton beams. Observing the following resonances: 0[sup [minus plus
Symmetry analysis for anisotropic field theories
Parra, Lorena; Vergara, J. David
2012-08-24
The purpose of this paper is to study with the help of Noether's theorem the symmetries of anisotropic actions for arbitrary fields which generally depend on higher order spatial derivatives, and to find the corresponding current densities and the Noether charges. We study in particular scale invariance and consider the cases of higher derivative extensions of the scalar field, electrodynamics and Chern-Simons theory.
The Mean-Field Flux Pinning Theory
NASA Astrophysics Data System (ADS)
Stejic, George
We develop the Mean-Field Flux Pinning Theory, designed to model the flux line lattice (FLL) as it interacts with itself, the flux pinning centers and the geometry of the superconductor. Like other mean-field theories, the mean-field flux pinning theory does not attempt to model the FLL completely. Instead, it utilizes a simplified model for the FLL, termed the mean-field FLL, in which the FLL is modelled as a continuous vector field rather than as discrete fluxons as in other theories. By so doing, the interactions of the FLL are greatly simplified and more easily modelled. One application of the mean-field flux pinning theory is to predict J_{c} from microstructural data, which we use to determine the optimal Nb-Ti microstructures with (1) alpha -Ti pinning centers and (2) Nb pinning centers. The microstructure is modelled on a grid in which the local values of T_{c} and kappa reflect the spatial distribution of the pinning centers and the superconductor. Using this model, we solve the G-L equations and calculate the pinning potential defined as the vortex free energy as a function of position. We conclude that the ideal Nb-Ti microstructure with alpha-Ti pinning centers would require 40 volume percent of alpha -Ti and have 6nm thick pinning centers. In the Nb pinning center case, the ideal microstructure requires 50 volume percent of Nb and would have 6nm pinning centers. Another application for the mean-field flux pinning theory is to model the FLL as it interacts with the penetrating magnetic fields within lambda of the superconducting surface. Using this theory, we study the effects of sample geometry on the FLL and J _{c} for the thin film geometry. We find that the FLL becomes increasingly distorted as the film thickness is reduced and that J_{c } increases sharply for dimensions less that lambda. These predictions are experimentally evaluated in Nb-Ti thin films. Our results show that J_{c} values as high as 1/3 of J_{d} and a strong orientational
Instruction in and about Small Group Discussion. Theory Into Practice.
ERIC Educational Resources Information Center
Book, Cassandra; Galvin, Kathleen
This booklet is one in a series designed to bridge the gap between theory and practice by suggesting specific classroom activities based on current educational theory and research. Approximately half of the booklet is devoted to a review of current research and theory concerning small group discussion and interaction. The second half presents…
Group-theoretical approach to Bloch electron in magnetic field problem
Cosic, Marko
2010-06-15
In this paper magnetic-translation group theory is extended to include full rotational symmetry of Hamiltonian. Proper generalization of small representation and star of the representation concepts are derived. Irreducible representations of magnetic-translation group and magnetic-space group are presented. Correct form of symmetrized basis function is derived, reflecting symmetry of the magnetic-point group. From viewpoint of group theory reduction of Hamiltonian symmetry group caused by magnetic field and splitting of energy levels is investigated.
Continuous wavelet transform in quantum field theory
NASA Astrophysics Data System (ADS)
Altaisky, M. V.; Kaputkina, N. E.
2013-07-01
We describe the application of the continuous wavelet transform to calculation of the Green functions in quantum field theory: scalar ϕ4 theory, quantum electrodynamics, and quantum chromodynamics. The method of continuous wavelet transform in quantum field theory, presented by Altaisky [Phys. Rev. D 81, 125003 (2010)] for the scalar ϕ4 theory, consists in substitution of the local fields ϕ(x) by those dependent on both the position x and the resolution a. The substitution of the action S[ϕ(x)] by the action S[ϕa(x)] makes the local theory into a nonlocal one and implies the causality conditions related to the scale a, the region causality [J. D. Christensen and L. Crane, J. Math. Phys. (N.Y.) 46, 122502 (2005)]. These conditions make the Green functions G(x1,a1,…,xn,an)=⟨ϕa1(x1)…ϕan(xn)⟩ finite for any given set of regions by means of an effective cutoff scale A=min(a1,…,an).
Dual field theories of quantum computation
NASA Astrophysics Data System (ADS)
Vanchurin, Vitaly
2016-06-01
Given two quantum states of N q-bits we are interested to find the shortest quantum circuit consisting of only one- and two- q-bit gates that would transfer one state into another. We call it the quantum maze problem for the reasons described in the paper. We argue that in a large N limit the quantum maze problem is equivalent to the problem of finding a semiclassical trajectory of some lattice field theory (the dual theory) on an N +1 dimensional space-time with geometrically flat, but topologically compact spatial slices. The spatial fundamental domain is an N dimensional hyper-rhombohedron, and the temporal direction describes transitions from an arbitrary initial state to an arbitrary target state and so the initial and final dual field theory conditions are described by these two quantum computational states. We first consider a complex Klein-Gordon field theory and argue that it can only be used to study the shortest quantum circuits which do not involve generators composed of tensor products of multiple Pauli Z matrices. Since such situation is not generic we call it the Z-problem. On the dual field theory side the Z-problem corresponds to massless excitations of the phase (Goldstone modes) that we attempt to fix using Higgs mechanism. The simplest dual theory which does not suffer from the massless excitation (or from the Z-problem) is the Abelian-Higgs model which we argue can be used for finding the shortest quantum circuits. Since every trajectory of the field theory is mapped directly to a quantum circuit, the shortest quantum circuits are identified with semiclassical trajectories. We also discuss the complexity of an actual algorithm that uses a dual theory prospective for solving the quantum maze problem and compare it with a geometric approach. We argue that it might be possible to solve the problem in sub-exponential time in 2 N , but for that we must consider the Klein-Gordon theory on curved spatial geometry and/or more complicated (than N -torus
Causality constraints in conformal field theory
NASA Astrophysics Data System (ADS)
Hartman, Thomas; Jain, Sachin; Kundu, Sandipan
2016-05-01
Causality places nontrivial constraints on QFT in Lorentzian signature, for example fixing the signs of certain terms in the low energy Lagrangian. In d dimensional conformal field theory, we show how such constraints are encoded in crossing symmetry of Euclidean correlators, and derive analogous constraints directly from the conformal bootstrap (analytically). The bootstrap setup is a Lorentzian four-point function corresponding to propagation through a shockwave. Crossing symmetry fixes the signs of certain log terms that appear in the conformal block expansion, which constrains the interactions of low-lying operators. As an application, we use the bootstrap to rederive the well known sign constraint on the (∂ ϕ)4 coupling in effective field theory, from a dual CFT. We also find constraints on theories with higher spin conserved currents. Our analysis is restricted to scalar correlators, but we argue that similar methods should also impose nontrivial constraints on the interactions of spinning operators.
Bipartite field theories from D-branes
NASA Astrophysics Data System (ADS)
Franco, Sebastián; Uranga, Angel
2014-04-01
We develop tools for determining the gauge theory resulting from a configuration of Type IIB D3-branes probing a non-compact, toric Calabi-Yau 3-fold, in the presence of additional flavor D7-branes with general embeddings. Two main ingredients of our approach are dimer models and mirror symmetry. D7-branes with general embeddings are obtained by recombination of elementary D7-brane constituents. These tools are then used to engineer a large set of Bipartite Field Theories, a class of 4d, = 1 quantum field theories defined by bipartite graphs on bordered Riemann surfaces. Several explicit examples, including infinite families of models, associated to both planar and non-planar graphs are presented.
Scalar field theory on fuzzy S 4
NASA Astrophysics Data System (ADS)
Medina, Julieta; O'Connor, Denjoe
2003-11-01
Scalar fields are studied on fuzzy S 4 and a solution is found for the elimination of the unwanted degrees of freedom that occur in the model. The resulting theory can be interpreted as a Kaluza-Klein reduction of Bbb CP3 to S 4 in the fuzzy context.
Cross Sections From Scalar Field Theory
NASA Technical Reports Server (NTRS)
Norbury, John W.; Dick, Frank; Norman, Ryan B.; Nasto, Rachel
2008-01-01
A one pion exchange scalar model is used to calculate differential and total cross sections for pion production through nucleon- nucleon collisions. The collisions involve intermediate delta particle production and decay to nucleons and a pion. The model provides the basic theoretical framework for scalar field theory and can be applied to particle production processes where the effects of spin can be neglected.
Field Theory of the Quantum Kicked Rotor
Altland, A.; Zirnbauer, M.R.
1996-11-01
The quantum kicked rotor is investigated by field theoretical methods. It is shown that the effective theory describing the long wavelength physics of the system is precisely the supersymmetric nonlinear {sigma} model for quasi-one-dimensional metallic wires. This proves that the analogy between chaotic systems with dynamical localization and disordered metals can indeed be exact. The role of symmetries is discussed.
Dirac-Kaehler Theory and Massless Fields
Pletyukhov, V. A.; Strazhev, V. I.
2010-03-24
Three massless limits of the Dirac-Kaehler theory are considered. It is shown that the Dirac-Kaehler equation for massive particles can be represented as a result of the gauge-invariant mixture (topological interaction) of the above massless fields.
Perturbative quantum gravity in double field theory
NASA Astrophysics Data System (ADS)
Boels, Rutger H.; Horst, Christoph
2016-04-01
We study perturbative general relativity with a two-form and a dilaton using the double field theory formulation which features explicit index factorisation at the Lagrangian level. Explicit checks to known tree level results are performed. In a natural covariant gauge a ghost-like scalar which contributes even at tree level is shown to decouple consistently as required by perturbative unitarity. In addition, a lightcone gauge is explored which bypasses the problem altogether. Using this gauge to study BCFW on-shell recursion, we can show that most of the D-dimensional tree level S-matrix of the theory, including all pure graviton scattering amplitudes, is reproduced by the double field theory. More generally, we argue that the integrand may be reconstructed from its single cuts and provide limited evidence for off-shell cancellations in the Feynman graphs. As a straightforward application of the developed technology double field theory-like expressions for four field string corrections are derived.
The Large N Limit of Superconformal Field Theories and Supergravity
NASA Astrophysics Data System (ADS)
Maldacena, Juan M.
We show that the large N limit of certain conformal field theories in various dimensions include in their Hilbert space a sector describing supergravity on the product of Anti-deSitter spacetimes, spheres and other compact manifolds. This is shown by taking some branes in the full M/string theory and then taking a low energy limit where the field theory on the brane decouples from the bulk. We observe that, in this limit, we can still trust the near horizon geometry for large N. The enhanced supersymmetries of the near horizon geometry correspond to the extra supersymmetry generators present in the superconformal group (as opposed to just the super-Poincare group). The 't Hooft limit of 4-d N =4 super-Yang-Mills at the conformal point is shown to contain strings: they are IIB strings. We conjecture that compactifications of M/string theory on various Anti-deSitter spacetimes are dual to various conformal field theories. This leads to a new proposal for a definition of M-theory which could be extended to include five non-compact dimensions.
The large N limit of superconformal field theories and supergravity
NASA Astrophysics Data System (ADS)
Maldacena, Juan
1999-07-01
We show that the large N limit of certain conformal field theories in various dimensions include in their Hilbert space a sector describing supergravity on the product of Anti-deSitter spacetimes, spheres and other compact manifolds. This is shown by taking some branes in the full M/string theory and then taking a low energy limit where the field theory on the brane decouples from the bulk. We observe that, in this limit, we can still trust the near horizon geometry for large N. The enhanced supersymmetries of the near horizon geometry correspond to the extra supersymmetry generators present in the superconformal group (as opposed to just the super-Poincare group). The 't Hooft limit of 3+1N=4 super-Yang-Mills at the conformal point is shown to contain strings: they are IIB strings. We conjecture that compactifications of M/string theory on various Anti-deSitter spacetimes is dual to various conformal field theories. This leads to a new proposal for a definition of M-theory which could be extended to include five non-compact dimensions.
Extending Gurwitsch's field theory of consciousness.
Yoshimi, Jeff; Vinson, David W
2015-07-01
Aron Gurwitsch's theory of the structure and dynamics of consciousness has much to offer contemporary theorizing about consciousness and its basis in the embodied brain. On Gurwitsch's account, as we develop it, the field of consciousness has a variable sized focus or "theme" of attention surrounded by a structured periphery of inattentional contents. As the field evolves, its contents change their status, sometimes smoothly, sometimes abruptly. Inner thoughts, a sense of one's body, and the physical environment are dominant field contents. These ideas can be linked with (and help unify) contemporary theories about the neural correlates of consciousness, inattention, the small world structure of the brain, meta-stable dynamics, embodied cognition, and predictive coding in the brain.
Group-III Nitride Field Emitters
NASA Technical Reports Server (NTRS)
Bensaoula, Abdelhak; Berishev, Igor
2008-01-01
Field-emission devices (cold cathodes) having low electron affinities can be fabricated through lattice-mismatched epitaxial growth of nitrides of elements from group III of the periodic table. Field emission of electrons from solid surfaces is typically utilized in vacuum microelectronic devices, including some display devices. The present field-emission devices and the method of fabricating them were developed to satisfy needs to reduce the cost of fabricating field emitters, make them compatible with established techniques for deposition of and on silicon, and enable monolithic integration of field emitters with silicon-based driving circuitry. In fabricating a device of this type, one deposits a nitride of one or more group-III elements on a substrate of (111) silicon or other suitable material. One example of a suitable deposition process is chemical vapor deposition in a reactor that contains plasma generated by use of electron cyclotron resonance. Under properly chosen growth conditions, the large mismatch between the crystal lattices of the substrate and the nitride causes strains to accumulate in the growing nitride film, such that the associated stresses cause the film to crack. The cracks lie in planes parallel to the direction of growth, so that the growing nitride film becomes divided into microscopic growing single-crystal columns. The outer ends of the fully-grown columns can serve as field-emission tips. By virtue of their chemical compositions and crystalline structures, the columns have low work functions and high electrical conductivities, both of which are desirable for field emission of electrons. From examination of transmission electron micrographs of a prototype device, the average column width was determined to be about 100 nm and the sharpness of the tips was determined to be characterized by a dimension somewhat less than 100 nm. The areal density of the columns was found to about 5 x 10(exp 9)/sq cm . about 4 to 5 orders of magnitude
C*-algebraic scattering theory and explicitly solvable quantum field theories
NASA Astrophysics Data System (ADS)
Warchall, Henry A.
1985-06-01
A general theoretical framework is developed for the treatment of a class of quantum field theories that are explicitly exactly solvable, but require the use of C*-algebraic techniques because time-dependent scattering theory cannot be constructed in any one natural representation of the observable algebra. The purpose is to exhibit mechanisms by which inequivalent representations of the observable algebra can arise in quantum field theory, in a setting free of other complications commonly associated with the specification of dynamics. One of two major results is the development of necessary and sufficient conditions for the concurrent unitary implementation of two automorphism groups in a class of quasifree representations of the algebra of the canonical commutation relations (CCR). The automorphism groups considered are induced by one-parameter groups of symplectic transformations on the classical phase space over which the Weyl algebra of the CCR is built; each symplectic group is conjugate by a fixed symplectic transformation to a one-parameter unitary group. The second result, an analog to the Birman-Belopol'skii theorem in two-Hilbert-space scattering theory, gives sufficient conditions for the existence of Mo/ller wave morphisms in theories with time-development automorphism groups of the above type. In a paper which follows, this framework is used to analyze a particular model system for which wave operators fail to exist in any natural representation of the observable algebra, but for which wave morphisms and an associated S matrix are easily constructed.
Thermodynamics of perfect fluids from scalar field theory
NASA Astrophysics Data System (ADS)
Ballesteros, Guillermo; Comelli, Denis; Pilo, Luigi
2016-07-01
The low-energy dynamics of relativistic continuous media is given by a shift-symmetric effective theory of four scalar fields. These scalars describe the embedding in spacetime of the medium and play the role of Stückelberg fields for spontaneously broken spatial and time translations. Perfect fluids are selected imposing a stronger symmetry group or reducing the field content to a single scalar. We explore the relation between the field theory description of perfect fluids to thermodynamics. By drawing the correspondence between the allowed operators at leading order in derivatives and the thermodynamic variables, we find that a complete thermodynamic picture requires the four Stückelberg fields. We show that thermodynamic stability plus the null-energy condition imply dynamical stability. We also argue that a consistent thermodynamic interpretation is not possible if any of the shift symmetries is explicitly broken.
Generalization of trinification to theories with 3N SU(3) gauge groups
Carone, Christopher D.
2005-04-01
We consider a natural generalization of trinification to theories with 3N SU(3) gauge groups. These theories have a simple moose representation and a gauge boson spectrum that can be interpreted via the deconstruction of a 5D theory with unified symmetry broken on a boundary. Although the matter and Higgs sectors of the theory have no simple extra-dimensional analog, gauge unification retains features characteristic of the 5D theory. We determine possible assignments of the matter and Higgs fields to unified multiplets and present theories that are viable alternatives to minimal trinified GUTs.
Symmetries, sum rules and constraints on effective field theories
NASA Astrophysics Data System (ADS)
Bellazzini, Brando; Martucci, Luca; Torre, Riccardo
2014-09-01
Using unitarity, analyticity and crossing symmetry, we derive universal sum rules for scattering amplitudes in theories invariant under an arbitrary symmetry group. The sum rules relate the coefficients of the energy expansion of the scattering amplitudes in the IR to total cross sections integrated all the way up to the UV. Exploiting the group structure of the symmetry, we systematically determine all the independent sum rules and positivity conditions on the expansion coefficients. For effective field theories the amplitudes in the IR are calculable and hence the sum rules set constraints on the parameters of the effective Lagrangian. We clarify the impact of gauging on the sum rules for Goldstone bosons in spontaneously broken gauge theories. We discuss explicit examples that are relevant for WW-scattering, composite Higgs models, and chiral perturbation theory. Certain sum rules based on custodial symmetry and its extensions provide constraints on the Higgs boson coupling to the electroweak gauge bosons.
Inflation and deformation of conformal field theory
Garriga, Jaume; Urakawa, Yuko E-mail: yurakawa@ffn.ub.es
2013-07-01
It has recently been suggested that a strongly coupled phase of inflation may be described holographically in terms of a weakly coupled quantum field theory (QFT). Here, we explore the possibility that the wave function of an inflationary universe may be given by the partition function of a boundary QFT. We consider the case when the field theory is a small deformation of a conformal field theory (CFT), by the addition of a relevant operator O, and calculate the primordial spectrum predicted in the corresponding holographic inflation scenario. Using the Ward-Takahashi identity associated with Weyl rescalings, we derive a simple relation between correlators of the curvature perturbation ζ and correlators of the deformation operator O at the boundary. This is done without specifying the bulk theory of gravitation, so that the result would also apply to cases where the bulk dynamics is strongly coupled. We comment on the validity of the Suyama-Yamaguchi inequality, relating the bi-spectrum and tri-spectrum of the curvature perturbation.
Alpha particles in effective field theory
Caniu, C.
2014-11-11
Using an effective field theory for alpha (α) particles at non-relativistic energies, we calculate the strong scattering amplitude modified by Coulomb corrections for a system of two αs. For the strong interaction, we consider a momentum-dependent interaction which, in contrast to an energy dependent interaction alone [1], could be more useful in extending the theory to systems with more than two α particles. We will present preliminary results of our EFT calculations for systems with two alpha particles.
Nonlinear quantum equations: Classical field theory
Rego-Monteiro, M. A.; Nobre, F. D.
2013-10-15
An exact classical field theory for nonlinear quantum equations is presented herein. It has been applied recently to a nonlinear Schrödinger equation, and it is shown herein to hold also for a nonlinear generalization of the Klein-Gordon equation. These generalizations were carried by introducing nonlinear terms, characterized by exponents depending on an index q, in such a way that the standard, linear equations, are recovered in the limit q→ 1. The main characteristic of this field theory consists on the fact that besides the usual Ψ(x(vector sign),t), a new field Φ(x(vector sign),t) needs to be introduced in the Lagrangian, as well. The field Φ(x(vector sign),t), which is defined by means of an additional equation, becomes Ψ{sup *}(x(vector sign),t) only when q→ 1. The solutions for the fields Ψ(x(vector sign),t) and Φ(x(vector sign),t) are found herein, being expressed in terms of a q-plane wave; moreover, both field equations lead to the relation E{sup 2}=p{sup 2}c{sup 2}+m{sup 2}c{sup 4}, for all values of q. The fact that such a classical field theory works well for two very distinct nonlinear quantum equations, namely, the Schrödinger and Klein-Gordon ones, suggests that this procedure should be appropriate for a wider class nonlinear equations. It is shown that the standard global gauge invariance is broken as a consequence of the nonlinearity.
Group-kinetic theory of turbulence
NASA Technical Reports Server (NTRS)
Tchen, C. M.
1986-01-01
The two phases are governed by two coupled systems of Navier-Stokes equations. The couplings are nonlinear. These equations describe the microdynamical state of turbulence, and are transformed into a master equation. By scaling, a kinetic hierarchy is generated in the form of groups, representing the spectral evolution, the diffusivity and the relaxation. The loss of memory in formulating the relaxation yields the closure. The network of sub-distributions that participates in the relaxation is simulated by a self-consistent porous medium, so that the average effect on the diffusivity is to make it approach equilibrium. The kinetic equation of turbulence is derived. The method of moments reverts it to the continuum. The equation of spectral evolution is obtained and the transport properties are calculated. In inertia turbulence, the Kolmogoroff law for weak coupling and the spectrum for the strong coupling are found. As the fluid analog, the nonlinear Schrodinger equation has a driving force in the form of emission of solitons by velocity fluctuations, and is used to describe the microdynamical state of turbulence. In order for the emission together with the modulation to participate in the transport processes, the non-homogeneous Schrodinger equation is transformed into a homogeneous master equation. By group-scaling, the master equation is decomposed into a system of transport equations, replacing the Bogoliubov system of equations of many-particle distributions. It is in the relaxation that the memory is lost when the ensemble of higher-order distributions is simulated by an effective porous medium. The closure is thus found. The kinetic equation is derived and transformed into the equation of spectral flow.
A master functional for quantum field theory
NASA Astrophysics Data System (ADS)
Anselmi, Damiano
2013-04-01
We study a new generating functional of one-particle irreducible diagrams in quantum field theory, called master functional, which is invariant under the most general perturbative changes of field variables. The usual functional Γ does not behave as a scalar under the transformation law inherited from its very definition as the Legendre transform of W=ln Z, although it does behave as a scalar under an unusual transformation law. The master functional, on the other hand, is the Legendre transform of an improved functional W with respect to the sources coupled to both elementary and composite fields. The inclusion of certain improvement terms in W and Z is necessary to make this new Legendre transform well defined. The master functional behaves as a scalar under the transformation law inherited from its very definition. Moreover, it admits a proper formulation, obtained extending the set of integrated fields to so-called proper fields, which allows us to work without passing through Z, W or Γ. In the proper formulation the classical action coincides with the classical limit of the master functional, and correlation functions and renormalization are calculated applying the usual diagrammatic rules to the proper fields. Finally, the most general change of field variables, including the map relating bare and renormalized fields, is a linear redefinition of the proper fields.
Relative entropies in conformal field theory.
Lashkari, Nima
2014-08-01
Relative entropy is a measure of distinguishability for quantum states, and it plays a central role in quantum information theory. The family of Renyi entropies generalizes to Renyi relative entropies that include, as special cases, most entropy measures used in quantum information theory. We construct a Euclidean path-integral approach to Renyi relative entropies in conformal field theory, then compute the fidelity and the relative entropy of states in one spatial dimension at zero and finite temperature using a replica trick. In contrast to the entanglement entropy, the relative entropy is free of ultraviolet divergences, and is obtained as a limit of certain correlation functions. The relative entropy of two states provides an upper bound on their trace distance.
Relative entropies in conformal field theory.
Lashkari, Nima
2014-08-01
Relative entropy is a measure of distinguishability for quantum states, and it plays a central role in quantum information theory. The family of Renyi entropies generalizes to Renyi relative entropies that include, as special cases, most entropy measures used in quantum information theory. We construct a Euclidean path-integral approach to Renyi relative entropies in conformal field theory, then compute the fidelity and the relative entropy of states in one spatial dimension at zero and finite temperature using a replica trick. In contrast to the entanglement entropy, the relative entropy is free of ultraviolet divergences, and is obtained as a limit of certain correlation functions. The relative entropy of two states provides an upper bound on their trace distance. PMID:25126908
Magnetic fields and density functional theory
Salsbury Jr., Freddie
1999-02-01
A major focus of this dissertation is the development of functionals for the magnetic susceptibility and the chemical shielding within the context of magnetic field density functional theory (BDFT). These functionals depend on the electron density in the absence of the field, which is unlike any other treatment of these responses. There have been several advances made within this theory. The first of which is the development of local density functionals for chemical shieldings and magnetic susceptibilities. There are the first such functionals ever proposed. These parameters have been studied by constructing functionals for the current density and then using the Biot-Savart equations to obtain the responses. In order to examine the advantages and disadvantages of the local functionals, they were tested numerically on some small molecules.
Quantitative field theory of the glass transition
Franz, Silvio; Jacquin, Hugo; Parisi, Giorgio; Urbani, Pierfrancesco; Zamponi, Francesco
2012-01-01
We develop a full microscopic replica field theory of the dynamical transition in glasses. By studying the soft modes that appear at the dynamical temperature, we obtain an effective theory for the critical fluctuations. This analysis leads to several results: we give expressions for the mean field critical exponents, and we analytically study the critical behavior of a set of four-points correlation functions, from which we can extract the dynamical correlation length. Finally, we can obtain a Ginzburg criterion that states the range of validity of our analysis. We compute all these quantities within the hypernetted chain approximation for the Gibbs free energy, and we find results that are consistent with numerical simulations. PMID:23112202
Effective field theory for lattice nuclei.
Barnea, N; Contessi, L; Gazit, D; Pederiva, F; van Kolck, U
2015-02-01
We show how nuclear effective field theory (EFT) and ab initio nuclear-structure methods can turn input from lattice quantum chromodynamics (LQCD) into predictions for the properties of nuclei. We argue that pionless EFT is the appropriate theory to describe the light nuclei obtained in LQCD simulations carried out at pion masses heavier than the physical pion mass. We solve the EFT using the effective-interaction hyperspherical harmonics and auxiliary-field diffusion Monte Carlo methods. Fitting the three leading-order EFT parameters to the deuteron, dineutron, and triton LQCD energies at m_{π}≈800 MeV, we reproduce the corresponding alpha-particle binding and predict the binding energies of mass-5 and mass-6 ground states. PMID:25699436
Effective Field Theory for Rydberg Polaritons.
Gullans, M J; Thompson, J D; Wang, Y; Liang, Q-Y; Vuletić, V; Lukin, M D; Gorshkov, A V
2016-09-01
We develop an effective field theory (EFT) to describe the few- and many-body propagation of one-dimensional Rydberg polaritons. We show that the photonic transmission through the Rydberg medium can be found by mapping the propagation problem to a nonequilibrium quench, where the role of time and space are reversed. We include effective range corrections in the EFT and show that they dominate the dynamics near scattering resonances in the presence of deep bound states. Finally, we show how the long-range nature of the Rydberg-Rydberg interactions induces strong effective N-body interactions between Rydberg polaritons. These results pave the way towards studying nonperturbative effects in quantum field theories using Rydberg polaritons. PMID:27661685
Higher spin double field theory: a proposal
NASA Astrophysics Data System (ADS)
Bekaert, Xavier; Park, Jeong-Hyuck
2016-07-01
We construct a double field theory coupled to the fields present in Vasiliev's equations. Employing the "semi-covariant" differential geometry, we spell a functional in which each term is completely covariant with respect to O(4, 4) T-duality, doubled diffeomorphisms, Spin(1, 3) local Lorentz symmetry and, separately, HS(4) higher spin gauge symmetry. We identify a minimal set of BPS-like conditions whose solutions automatically satisfy the full Euler-Lagrange equations. As such a solution, we derive a linear dilaton vacuum. With extra algebraic constraints further supplemented, the BPS-like conditions reduce to the bosonic Vasiliev equations.
Heavy Quarks, QCD, and Effective Field Theory
Thomas Mehen
2012-10-09
The research supported by this OJI award is in the area of heavy quark and quarkonium production, especially the application Soft-Collinear E ective Theory (SCET) to the hadronic production of quarkonia. SCET is an e ffective theory which allows one to derive factorization theorems and perform all order resummations for QCD processes. Factorization theorems allow one to separate the various scales entering a QCD process, and in particular, separate perturbative scales from nonperturbative scales. The perturbative physics can then be calculated using QCD perturbation theory. Universal functions with precise fi eld theoretic de nitions describe the nonperturbative physics. In addition, higher order perturbative QCD corrections that are enhanced by large logarithms can be resummed using the renormalization group equations of SCET. The applies SCET to the physics of heavy quarks, heavy quarkonium, and similar particles.
Bosonic Dynamical Mean-Field Theory
NASA Astrophysics Data System (ADS)
Snoek, Michiel; Hofstetter, Walter
2013-02-01
We derive the bosonic dynamical mean-field equations for bosonic atoms in optical lattices with arbitrary lattice geometry. The equations are presented as a systematic expansion in 1/z, z being the number of lattice neighbours. Hence the theory is applicable in sufficiently high-dimensional lattices. We apply the method to a two-component mixture, for which a rich phase diagram with spin order is revealed.
Backreacted axion field ranges in string theory
NASA Astrophysics Data System (ADS)
Baume, Florent; Palti, Eran
2016-08-01
String theory axions are interesting candidates for fields whose potential might be controllable over super-Planckian field ranges and therefore as possible candidates for inflatons in large field inflation. Axion monodromy scenarios are setups where the axion shift symmetry is broken by some effect such that the axion can traverse a large number of periods potentially leading to super-Planckian excursions. We study such scenarios in type IIA string theory where the axion shift symmetry is broken by background fluxes. In particular we calculate the backreaction of the energy density induced by the axion vacuum expectation value on its own field space metric. We find universal behaviour for all the compactifications studied where up to a certain critical axion value there is only a small backreaction effect. Beyond the critical value the backreaction is strong and implies that the proper field distance as measured by the backreacted metric increases at best logarithmically with the axion vev, thereby placing strong limitations on extending the field distance any further. The critical axion value can be made arbitrarily large by the choice of fluxes. However the backreaction of these fluxes on the axion field space metric ensures a precise cancellation such that the proper field distance up to the critical axion value is flux independent and remains sub-Planckian. We also study an axion alignment scenario for type IIA compactifications on a twisted torus with four fundamental axions mixing to leave an axion with an effective decay constant which is flux dependent. There is a choice of fluxes for which the alignment parameter controlling the effective decay constant is unconstrained by tadpoles and can in principle lead to an arbitrarily large effective decay constant. However we show that these fluxes backreact on the fundamental decay constants so as to precisely cancel any enhancement leaving a sub-Planckian effective decay constant.
Reading Discussion Groups for Teachers: Connecting Theory to Practice
ERIC Educational Resources Information Center
Fenton-Smith, Ben; Stillwell, Christopher
2011-01-01
This article explores how teachers can engage with ideas (research findings, theory, and professional knowledge) through participation in a reading discussion group. Focusing on one group formed by English language teachers at a Japanese university, the study employs survey data, attendance statistics, and observational notes regarding the group's…
Replicating Small Group Research Using the Functional Theory.
ERIC Educational Resources Information Center
Cragan, John F.; Wright, David W.
A replication study tested functional theory utilizing untrained full-fledged groups. One hundred forty undergraduate students who were enrolled in a small group communication course at a large midwestern university participated in small group discussions analyzing a plagiarism case used in an original study by R. Y. Hirokawa. Results indicated…
The effective field theory of inflation
NASA Astrophysics Data System (ADS)
Cheung, Clifford; Fitzpatrick, A. Liam; Kaplan, Jared; Senatore, Leonardo; Creminelli, Paolo
2008-03-01
We study the effective field theory of inflation, i.e. the most general theory describing the fluctuations around a quasi de Sitter background, in the case of single field models. The scalar mode can be eaten by the metric by going to unitary gauge. In this gauge, the most general theory is built with the lowest dimension operators invariant under spatial diffeomorphisms, like g^{00} and K_{mu nu}, the extrinsic curvature of constant time surfaces. This approach allows us to characterize all the possible high energy corrections to simple slow-roll inflation, whose sizes are constrained by experiments. Also, it describes in a common language all single field models, including those with a small speed of sound and Ghost Inflation, and it makes explicit the implications of having a quasi de Sitter background. The non-linear realization of time diffeomorphisms forces correlation among different observables, like a reduced speed of sound and an enhanced level of non-Gaussianity.
A Grounded Theory of Western-Trained Asian Group Leaders Leading Groups in Asia
ERIC Educational Resources Information Center
Taephant, Nattasuda; Rubel, Deborah; Champe, Julia
2015-01-01
This grounded theory research explored the experiences of Western-trained Asian group leaders leading groups in Asia. A total of 6 participants from Japan, Taiwan, and Thailand were interviewed 3 times over 9 months. The recursive process of data collection and analysis yielded substantive theory describing the participants' process of…
Practicing Social Movement Theory in Case Study Groups
ERIC Educational Resources Information Center
Ormrod, James S.
2011-01-01
This article evaluates the use of a "case study group" method for teaching social movement theory. The aim was to give students the opportunity to practice theorizing actively rather than simply learning theory passively. The method provides this by requiring students to undertake case studies on social movements of their choice for the duration…
Theory of gain in group-III nitride lasers
Chow, W.W.; Wright, A.F.; Girndt, A.
1997-06-01
A microscopic theory of gain in a group-III nitride quantum well laser is presented. The approach, which treats carrier correlations at the level of quantum kinetic theory, gives a consistent account of plasma and excitonic effects in an inhomogeneously broadened system.
An Intuitive Approach to Group Representation Theory, II.
ERIC Educational Resources Information Center
Wolbarst, A. B.
1979-01-01
This is the second of several papers which attempts to introduce group representation theory to students of molecular or solid-state physics in as intuitive and simple a fashion as possible. (Author/BB)
NASA Astrophysics Data System (ADS)
Krajewski, Thomas; Toriumi, Reiko
2016-09-01
In this paper, we use the exact renormalisation in the context of tensor models and group field theories. As a byproduct, we rederive Gaußian universality for random tensors and provide a general power counting for Abelian tensorial field theories with a closure constraint, leading us to a only five renormalisable theories.
Effective field theory of cosmological perturbations
NASA Astrophysics Data System (ADS)
Piazza, Federico; Vernizzi, Filippo
2013-11-01
The effective field theory of cosmological perturbations stems from considering a cosmological background solution as a state displaying spontaneous breaking of time translations and (adiabatic) perturbations as the related Nambu-Goldstone modes. With this insight, one can systematically develop a theory for the cosmological perturbations during inflation and, with minor modifications, also describe in full generality the gravitational interactions of dark energy, which are relevant for late-time cosmology. The formalism displays a unique set of Lagrangian operators containing an increasing number of cosmological perturbations and derivatives. We give an introductory description of the unitary gauge formalism for theories with broken gauge symmetry—that allows us to write down the most general Lagrangian—and of the Stückelberg ‘trick’—that allows to recover gauge invariance and to make the scalar field explicit. We show how to apply this formalism to gravity and cosmology and we reproduce the detailed analysis of the action in the ADM variables. We also review some basic applications to inflation and dark energy.
Aspects of hot Galilean field theory
NASA Astrophysics Data System (ADS)
Jensen, Kristan
2015-04-01
We reconsider general aspects of Galilean-invariant thermal field theory. Using the proposal of our companion paper, we recast non-relativistic hydrodynamics in a manifestly covariant way and couple it to a background spacetime. We examine the concomitant consequences for the thermal partition functions of Galilean theories on a time-independent, but weakly curved background. We work out both the hydrodynamics and partition functions in detail for the example of parity-violating normal fluids in two dimensions to first order in the gradient expansion, finding results that differ from those previously reported in the literature. As for relativistic field theories, the equality-type constraints imposed by the existence of an entropy current appear to be in one-to-one correspondence with those arising from the existence of a hydrostatic partition function. Along the way, we obtain a number of useful results about non-relativistic hydrodynamics, including a manifestly boost-invariant presentation thereof, simplified Ward identities, the systematics of redefinitions of the fluid variables, and the positivity of entropy production.
Inhomogeneous field theory inside the arctic circle
NASA Astrophysics Data System (ADS)
Allegra, Nicolas; Dubail, Jérôme; Stéphan, Jean-Marie; Viti, Jacopo
2016-05-01
Motivated by quantum quenches in spin chains, a one-dimensional toy-model of fermionic particles evolving in imaginary-time from a domain-wall initial state is solved. The main interest of this toy-model is that it exhibits the arctic circle phenomenon, namely a spatial phase separation between a critically fluctuating region and a frozen region. Large-scale correlations inside the critical region are expressed in terms of correlators in a (euclidean) two-dimensional massless Dirac field theory. It is observed that this theory is inhomogenous: the metric is position-dependent, so it is in fact a Dirac theory in curved space. The technique used to solve the toy-model is then extended to deal with the transfer matrices of other models: dimers on the honeycomb and square lattice, and the six-vertex model at the free fermion point (Δ =0 ). In all cases, explicit expressions are given for the long-range correlations in the critical region, as well as for the underlying Dirac action. Although the setup developed here is heavily based on fermionic observables, the results can be translated into the language of height configurations and of the gaussian free field, via bosonization. Correlations close to the phase boundary and the generic appearance of Airy processes in all these models are also briefly revisited in the appendix.
Causality constraints in conformal field theory
Hartman, Thomas; Jain, Sachin; Kundu, Sandipan
2016-05-17
Causality places nontrivial constraints on QFT in Lorentzian signature, for example fixing the signs of certain terms in the low energy Lagrangian. In d dimensional conformal field theory, we show how such constraints are encoded in crossing symmetry of Euclidean correlators, and derive analogous constraints directly from the conformal bootstrap (analytically). The bootstrap setup is a Lorentzian four-point function corresponding to propagation through a shockwave. Crossing symmetry fixes the signs of certain log terms that appear in the conformal block expansion, which constrains the interactions of low-lying operators. As an application, we use the bootstrap to rederive the well knownmore » sign constraint on the (Φ)4 coupling in effective field theory, from a dual CFT. We also find constraints on theories with higher spin conserved currents. As a result, our analysis is restricted to scalar correlators, but we argue that similar methods should also impose nontrivial constraints on the interactions of spinning operators« less
Effective field theory with two Higgs doublets
NASA Astrophysics Data System (ADS)
Crivellin, Andreas; Ghezzi, Margherita; Procura, Massimiliano
2016-09-01
In this article we extend the effective field theory framework describing new physics effects to the case where the underlying low-energy theory is a Two-Higgs-Doublet model. We derive a complete set of independent operators up to dimension six assuming a Z 2-invariant CP-conserving Higgs potential. The effects on Higgs and gauge boson masses, mixing angles in the Higgs sector as well as couplings to fermions and gauge bosons are computed. At variance with the case of a single Higgs doublet, we find that pair production of SM-like Higgses, arising through dimension-six operators, is not fixed by fermion-fermion-Higgs couplings and can therefore be sizable.
The effective field theory of dark energy
NASA Astrophysics Data System (ADS)
Gubitosi, Giulia; Piazza, Federico; Vernizzi, Filippo
2013-02-01
We propose a universal description of dark energy and modified gravity that includes all single-field models. By extending a formalism previously applied to inflation, we consider the metric universally coupled to matter fields and we write in terms of it the most general unitary gauge action consistent with the residual unbroken symmetries of spatial diffeomorphisms. Our action is particularly suited for cosmological perturbation theory: the background evolution depends on only three operators. All other operators start at least at quadratic order in the perturbations and their effects can be studied independently and systematically. In particular, we focus on the properties of a few operators which appear in non-minimally coupled scalar-tensor gravity and galileon theories. In this context, we study the mixing between gravity and the scalar degree of freedom. We assess the quantum and classical stability, derive the speed of sound of fluctuations and the renormalization of the Newton constant. The scalar can always be de-mixed from gravity at quadratic order in the perturbations, but not necessarily through a conformal rescaling of the metric. We show how to express covariant field-operators in our formalism and give several explicit examples of dark energy and modified gravity models in our language. Finally, we discuss the relation with the covariant EFT methods recently appeared in the literature.
Toward a quantum theory of tachyon fields
NASA Astrophysics Data System (ADS)
Schwartz, Charles
2016-03-01
We construct momentum space expansions for the wave functions that solve the Klein-Gordon and Dirac equations for tachyons, recognizing that the mass shell for such fields is very different from what we are used to for ordinary (slower than light) particles. We find that we can postulate commutation or anticommutation rules for the operators that lead to physically sensible results: causality, for tachyon fields, means that there is no connection between space-time points separated by a timelike interval. Calculating the conserved charge and four-momentum for these fields allows us to interpret the number operators for particles and antiparticles in a consistent manner; and we see that helicity plays a critical role for the spinor field. Some questions about Lorentz invariance are addressed and some remain unresolved; and we show how to handle the group representation for tachyon spinors.
QCD unitarity constraints on Reggeon Field Theory
NASA Astrophysics Data System (ADS)
Kovner, Alex; Levin, Eugene; Lublinsky, Michael
2016-08-01
We point out that the s-channel unitarity of QCD imposes meaningful constraints on a possible form of the QCD Reggeon Field Theory. We show that neither the BFKL nor JIMWLK nor Braun's Hamiltonian satisfy the said constraints. In a toy, zero transverse dimensional case we construct a model that satisfies the analogous constraint and show that at infinite energy it indeed tends to a "black disk limit" as opposed to the model with triple Pomeron vertex only, routinely used as a toy model in the literature.
Theory of microemulsions in a gravitational field
NASA Technical Reports Server (NTRS)
Jeng, J. F.; Miller, Clarence A.
1989-01-01
A theory of microemulsions developed previously is extended to include the effect of a gravitational field. It predicts variation with position of drop size, drop volume fraction, and area per molecule in the surfactant films within a microemulsion phase. Variation in volume fraction is greatest and occurs in such a way that oil content increases with increasing elevation, as has been found experimentally. Large composition variations are predicted within a middle phase microemulsion near optimal conditions because inversion from the water-continuous to the oil-continuous arrangement occurs with increasing elevation. Generally speaking, gravity reduces solubilization within microemulsions and promotes separation of excess phases.
Temperature Gradient Field Theory of Nucleation
NASA Astrophysics Data System (ADS)
Das, S.; Ain, W. Q.; Azhari, A.; Prasada Rao, A. K.
2016-02-01
According to the proposed theory, ceramic particles present in molten metal, lose heat at a slower rate than the metallic liquid during cooling. Such condition results in the formation of a spherical thermal gradient field (TGF) around each particle. Hence, the interstitials (low temperature) of such TGFs are the regions to reach the nucleation temperature first, owing to low energy barrier than the liquid-particle interface (higher temperature). Analytics also indicate that the nucleation rate is higher at the TGF interstitials, than at the liquid-particle interface. Such TGF network results in simultaneous nucleation throughout the system, resulting in grain refinement.
Purely cubic action for string field theory
NASA Technical Reports Server (NTRS)
Horowitz, G. T.; Lykken, J.; Rohm, R.; Strominger, A.
1986-01-01
It is shown that Witten's (1986) open-bosonic-string field-theory action and a closed-string analog can be written as a purely cubic interaction term. The conventional form of the action arises by expansion around particular solutions of the classical equations of motion. The explicit background dependence of the conventional action via the Becchi-Rouet-Stora-Tyutin operator is eliminated in the cubic formulation. A closed-form expression is found for the full nonlinear gauge-transformation law.
A matrix model from string field theory
NASA Astrophysics Data System (ADS)
Zeze, Syoji
2016-09-01
We demonstrate that a Hermitian matrix model can be derived from level truncated open string field theory with Chan-Paton factors. The Hermitian matrix is coupled with a scalar and U(N) vectors which are responsible for the D-brane at the tachyon vacuum. Effective potential for the scalar is evaluated both for finite and large N. Increase of potential height is observed in both cases. The large N matrix integral is identified with a system of N ZZ branes and a ghost FZZT brane.
The Application of Games Theory to Group Project Assessment.
ERIC Educational Resources Information Center
Pitt, M. J.
2000-01-01
Application of game theory to small-group project evaluation in higher education instruction finds that the best strategy for students wishing high grades may not be a strategy that promotes teamwork and cooperation. Suggests that putting students into groups may randomly disadvantage some students relative to others, producing serious unfairness…
Supporting Alternative Strategies for Learning Chemical Applications of Group Theory
ERIC Educational Resources Information Center
Southam, Daniel C.; Lewis, Jennifer E.
2013-01-01
A group theory course for chemists was taught entirely with process oriented guided inquiry learning (POGIL) to facilitate alternative strategies for learning. Students completed a test of one aspect of visuospatial aptitude to determine their individual approaches to solving spatial tasks, and were sorted into groups for analysis on the basis of…
Pauli-Villars regulatization of supergravity and field theory anomalies
Gaillard, M.K.
1995-06-01
A procedure for Pauli-Villars regularization of locally and globally supersymmetric theories is described. Implications for specific theories, especially those obtained from superstrings, are discussed with emphasis on the role of field theory anomalies.
PT-Symmetric Quantum Field Theory
NASA Astrophysics Data System (ADS)
Bender, Carl M.
2011-09-01
In 1998 it was discovered that the requirement that a Hamiltonian be Dirac Hermitian (H = H†) can be weakened and generalized to the requirement that a Hamiltonian be PT symmetric ([H,PT] = 0); that is, invariant under combined space reflection and time reversal. Weakening the constraint of Hermiticity allows one to consider new kinds of physically acceptable Hamiltonians and, in effect, it amounts to extending quantum mechanics from the real (Hermitian) domain into the complex domain. Much work has been done on the analysis of various PT-symmetric quantum-mechanical models. However, only very little analysis has been done on PT-symmetric quantum-field-theoretic models. Here, we describe some of what has been done in the context of PT-symmetric quantum field theory and describe some possible fundamental applications.
Causality Is Inconsistent With Quantum Field Theory
Wolf, Fred Alan
2011-11-29
Causality in quantum field theory means the vanishing of commutators for spacelike separated fields (VCSSF). I will show that VCSSF is not tenable. For VCSSF to be tenable, and therefore, to have both retarded and advanced propagators vanish in the elsewhere, a superposition of negative energy antiparticle and positive energy particle propagators, traveling forward in time, and a superposition of negative energy particle and positive energy antiparticle propagators, traveling backward in time, are required. Hence VCSSF predicts non-vanishing probabilities for both negative energy particles in the forward-through-time direction and positive energy antiparticles in the backwards-through-time direction. Therefore, since VCSSF is unrealizable in a stable universe, tachyonic propagation must occur in denial of causality.
Conformal field theory of critical Casimir forces
NASA Astrophysics Data System (ADS)
Emig, Thorsten; Bimonte, Giuseppe; Kardar, Mehran
2015-03-01
Thermal fluctuations of a critical system induce long-ranged Casimir forces between objects that couple to the underlying field. For two dimensional conformal field theories (CFT) we derive exact results for the Casimir interaction for a deformed strip and for two compact objects of arbitrary shape in terms of the free energy of a standard region (circular ring or flat strip) whose dimension is determined by the mutual capacitance of two conductors with the objects' shape; and a purely geometric energy that is proportional to conformal charge of the CFT, but otherwise super-universal in that it depends only on the shapes and is independent of boundary conditions and other details. The effect of inhomogenous boundary conditions is also discussed.
A geometrical approach to two-dimensional Conformal Field Theory
NASA Astrophysics Data System (ADS)
Dijkgraaf, Robertus Henricus
1989-09-01
This thesis is organized in the following way. In Chapter 2 we will give a brief introduction to conformal field theory along the lines of standard quantum field theory, without any claims to originality. We introduce the important concepts of the stress-energy tensor, the Virasoro algebra, and primary fields. The general principles are demonstrated by fermionic and bosonic free field theories. This also allows us to discuss some general aspects of moduli spaces of CFT's. In particular, we describe in some detail the space of iiiequivalent toroidal comi)actificalions, giving examples of the quantum equivalences that we already mentioned. In Chapter 3 we will reconsider general quantum field theory from a more geometrical point of view, along the lines of the so-called operator formalism. Crucial to this approach will be the consideration of topology changing amplitudes. After a simple application to 2d topological theories, we proceed to give our second introduction to CFT, stressing the geometry behind it. In Chapter 4 the so-called rational conformal field theories are our object of study. These special CFT's have extended symmetries with only a finite number of representations. If an interpretation as non-linear sigma model exists, this extra symmetry can be seen as a kind of resonance effect due to the commensurability of the size of the string and the target space-time. The structure of rational CFT's is extremely rigid, and one of our results will be that the operator content of these models is—up to some discrete choices—completely determined by the symmetry algebra. The study of rational models is in its rigidity very analogous to finite group theory. In Chapter 5 this analogy is further pursued and substantiated. We will show how one can construct from general grounds rational conformal field theories from finite groups. These models are abstract versions of non-linear o-models describing string propagation on 'orbifoids.' An orbifold is a singular
Ramond equations of motion in superstring field theory
NASA Astrophysics Data System (ADS)
Erler, Theodore; Konopka, Sebastian; Sachs, Ivo
2015-11-01
We extend the recently constructed NS superstring field theories in the small Hilbert space to give classical field equations for all superstring theories, including Ramond sectors. We also comment on the realization of supersymmetry in this framework.
Anomaly cancelation in field theory and F-theory on a circle
NASA Astrophysics Data System (ADS)
Grimm, Thomas W.; Kapfer, Andreas
2016-05-01
We study the manifestation of local gauge anomalies of four- and six-dimensional field theories in the lower-dimensional Kaluza-Klein theory obtained after circle compactification. We identify a convenient set of transformations acting on the whole tower of massless and massive states and investigate their action on the low-energy effective theories in the Coulomb branch. The maps employ higher-dimensional large gauge transformations and precisely yield the anomaly cancelation conditions when acting on the one-loop induced Chern-Simons terms in the three- and five-dimensional effective theory. The arising symmetries are argued to play a key role in the study of the M-theory to F-theory limit on Calabi-Yau manifolds. For example, using the fact that all fully resolved F-theory geometries inducing multiple Abelian gauge groups or non-Abelian groups admit a certain set of symmetries, we are able to generally show the cancelation of pure Abelian or pure non-Abelian anomalies in these models.
Continuum regularization of quantum field theory
Bern, Z.
1986-04-01
Possible nonperturbative continuum regularization schemes for quantum field theory are discussed which are based upon the Langevin equation of Parisi and Wu. Breit, Gupta and Zaks made the first proposal for new gauge invariant nonperturbative regularization. The scheme is based on smearing in the ''fifth-time'' of the Langevin equation. An analysis of their stochastic regularization scheme for the case of scalar electrodynamics with the standard covariant gauge fixing is given. Their scheme is shown to preserve the masslessness of the photon and the tensor structure of the photon vacuum polarization at the one-loop level. Although stochastic regularization is viable in one-loop electrodynamics, two difficulties arise which, in general, ruins the scheme. One problem is that the superficial quadratic divergences force a bottomless action for the noise. Another difficulty is that stochastic regularization by fifth-time smearing is incompatible with Zwanziger's gauge fixing, which is the only known nonperturbaive covariant gauge fixing for nonabelian gauge theories. Finally, a successful covariant derivative scheme is discussed which avoids the difficulties encountered with the earlier stochastic regularization by fifth-time smearing. For QCD the regularized formulation is manifestly Lorentz invariant, gauge invariant, ghost free and finite to all orders. A vanishing gluon mass is explicitly verified at one loop. The method is designed to respect relevant symmetries, and is expected to provide suitable regularization for any theory of interest. Hopefully, the scheme will lend itself to nonperturbative analysis. 44 refs., 16 figs.
Entanglement negativity in quantum field theory.
Calabrese, Pasquale; Cardy, John; Tonni, Erik
2012-09-28
We develop a systematic method to extract the negativity in the ground state of a 1+1 dimensional relativistic quantum field theory, using a path integral formalism to construct the partial transpose ρ(A)(T(2) of the reduced density matrix of a subsystem [formula: see text], and introducing a replica approach to obtain its trace norm which gives the logarithmic negativity E=ln//ρ(A)(T(2))//. This is shown to reproduce standard results for a pure state. We then apply this method to conformal field theories, deriving the result E~(c/4)ln[ℓ(1)ℓ(2)/(ℓ(1)+ℓ(2))] for the case of two adjacent intervals of lengths ℓ(1), ℓ(2) in an infinite system, where c is the central charge. For two disjoint intervals it depends only on the harmonic ratio of the four end points and so is manifestly scale invariant. We check our findings against exact numerical results in the harmonic chain.
The effective field theory treatment of quantum gravity
Donoghue, John F.
2012-09-24
This is a pedagogical introduction to the treatment of quantum general relativity as an effective field theory. It starts with an overview of the methods of effective field theory and includes an explicit example. Quantum general relativity matches this framework and I discuss gravitational examples as well as the limits of the effective field theory. I also discuss the insights from effective field theory on the gravitational effects on running couplings in the perturbative regime.
Time-dependent perturbation theory in quantum mechanics and the renormalization group
NASA Astrophysics Data System (ADS)
Bhattacharjee, J. K.; Ray, D. S.
2016-06-01
Time-dependent perturbation theory in quantum mechanics is divergent at long times when the perturbation induces a resonance between two eigenstates of the unperturbed Hamiltonian. Divergences in perturbation theory are also common in quantum field theory and in critical phenomena. The renormalization group (RG) was designed to deal with these divergences. In the last two decades, this procedure has been extended to dynamical systems where the perturbation theory diverges in the long-time limit. In this article, we first review the connection between RG in the context of field theory and RG in the context of dynamical systems. We then show that the long-time divergence in the resonant situation in the time-dependent perturbation theory in quantum mechanics can be removed by using a RG-aided calculational scheme.
Investigations of low-dimensional field theories
NASA Astrophysics Data System (ADS)
Shifrin, Leonid
Spontaneous chiral symmetry breaking plays an important role in the low-energy dynamics of QCD. The nonzero chiral condensate is related to the non-zero density of small Dirac eigenvalues through the Banks-Casher relation. Further, the low-energy QCD Dirac spectrum has to satisfy a family of universal consistency relations called Leutwyler-Smilga (LS) spectral sum rules. We discuss these sum rules in the closely related to QCD but much simpler 2-dimensional Schwinger model. The dynamics of the two theories share chiral anomaly, topologically non-trivial vacuum, instantons, dynamical mass generation and confinement. While LS sum rules are the same for both theories, in the Schwinger model it is possible to achieve a more detailed microscopic understanding of them. We give three different derivations of LS sum rules in the Schwinger Model. The first is based on the clustering property of fermionic correlators and is also valid for 1-flavor QCD. The second is an exact microscopic (field theory) derivation. The third relies on 2D bosonization. Next, we discuss the clustering property for the multi-flavor QCD. It is shown that standard clustering is violated in the chiral limit, and a modified clustering relation is derived. Then we consider multi-flavor Schwinger model, and discuss the spectral density and mass dependence of the chiral condensate in the thermodynamic limit. The relation to Random Fermion models used in condensed matter physics is also discussed here. Relations with the Random Matrix Theory and the so called spectral duality are discussed next. Finally, we comment briefly on the remaining unsolved problems and relevance to lattice studies.
Quantum field theory of K-mouflage
NASA Astrophysics Data System (ADS)
Brax, Philippe; Valageas, Patrick
2016-08-01
We consider K-mouflage models, which are K-essence theories coupled to matter. We analyze their quantum properties and in particular the quantum corrections to the classical Lagrangian. We setup the renormalization program for these models and show that, contrary to renormalizable field theories where renormalization by infinite counterterms can be performed in one step, K-mouflage theories involve a recursive construction whereby each set of counterterms introduces new divergent quantum contributions which in turn must be subtracted by new counterterms. This tower of counterterms can be in principle constructed step by step by recursion and allows one to calculate the finite renormalized action of the model. In particular, it can be checked that the classical action is not renormalized and that the finite corrections to the renormalized action contain only higher-derivative operators. We concentrate then on the regime where calculability is ensured, i.e., when the corrections to the classical action are negligible. We establish an operational criterion for classicality and show that this is satisfied in cosmological and astrophysical situations for (healthy) K-mouflage models which pass the solar system tests. These results rely on perturbation theory around a background and are only valid when the background configuration is quantum stable. We analyze the quantum stability of astrophysical and cosmological backgrounds and find that models that pass the solar system tests are quantum stable. We then consider the possible embedding of the K-mouflage models in an UV completion. We find that the healthy models which pass the solar system tests all violate the positivity constraint which would follow from the unitarity of the putative UV completion, implying that these healthy K-mouflage theories have no UV completion. We then analyze their behavior at high energy, and we find that the classicality criterion is satisfied in the vicinity of a high-energy collision
BOOK REVIEW: Classical Solutions in Quantum Field Theory Classical Solutions in Quantum Field Theory
NASA Astrophysics Data System (ADS)
Mann, Robert
2013-02-01
Quantum field theory has evolved from its early beginnings as a tool for understanding the interaction of light with matter into a rather formidable technical paradigm, one that has successfully provided the mathematical underpinnings of all non-gravitational interactions. Over the eight decades since it was first contemplated the methods have become increasingly more streamlined and sophisticated, yielding new insights into our understanding of the subatomic world and our abilities to make clear and precise predictions. Some of the more elegant methods have to do with non-perturbative and semiclassical approaches to the subject. The chief players here are solitons, instantons, and anomalies. Over the past three decades there has been a steady rise in our understanding of these objects and of our ability to calculate their effects and implications for the rest of quantum field theory. This book is a welcome contribution to this subject. In 12 chapters it provides a clear synthesis of the key developments in these subjects at a level accessible to graduate students that have had an introductory course to quantum field theory. In the author's own words it provides both 'a survey and an overview of this field'. The first half of the book concentrates on solitons--kinks, vortices, and magnetic monopoles--and their implications for the subject. The reader is led first through the simplest models in one spatial dimension, into more sophisticated cases that required more advanced topological methods. The author does quite a nice job of introducing the various concepts as required, and beginning students should be able to get a good grasp of the subject directly from the text without having to first go through the primary literature. The middle part of the book deals with the implications of these solitons for both cosmology and for duality. While the cosmological discussion is quite nice, the discussion on BPS solitons, supersymmetry and duality is rather condensed. It is
The monster sporadic group and a theory underlying superstring models
Chapline, G.
1996-09-01
The pattern of duality symmetries acting on the states of compactified superstring models reinforces an earlier suggestion that the Monster sporadic group is a hidden symmetry for superstring models. This in turn points to a supersymmetric theory of self-dual and anti-self-dual K3 manifolds joined by Dirac strings and evolving in a 13 dimensional spacetime as the fundamental theory. In addition to the usual graviton and dilaton this theory contains matter-like degrees of freedom resembling the massless states of the heterotic string, thus providing a completely geometric interpretation for ordinary matter. 25 refs.
Power counting and Wilsonian renormalization in nuclear effective field theory
NASA Astrophysics Data System (ADS)
Valderrama, Manuel Pavón
2016-05-01
Effective field theories are the most general tool for the description of low energy phenomena. They are universal and systematic: they can be formulated for any low energy systems we can think of and offer a clear guide on how to calculate predictions with reliable error estimates, a feature that is called power counting. These properties can be easily understood in Wilsonian renormalization, in which effective field theories are the low energy renormalization group evolution of a more fundamental — perhaps unknown or unsolvable — high energy theory. In nuclear physics they provide the possibility of a theoretically sound derivation of nuclear forces without having to solve quantum chromodynamics explicitly. However there is the problem of how to organize calculations within nuclear effective field theory: the traditional knowledge about power counting is perturbative but nuclear physics is not. Yet power counting can be derived in Wilsonian renormalization and there is already a fairly good understanding of how to apply these ideas to non-perturbative phenomena and in particular to nuclear physics. Here we review a few of these ideas, explain power counting in two-nucleon scattering and reactions with external probes and hint at how to extend the present analysis beyond the two-body problem.
Group theory and biomolecular conformation: I. Mathematical and computational models
Chirikjian, Gregory S
2010-01-01
Biological macromolecules, and the complexes that they form, can be described in a variety of ways ranging from quantum mechanical and atomic chemical models, to coarser grained models of secondary structure and domains, to continuum models. At each of these levels, group theory can be used to describe both geometric symmetries and conformational motion. In this survey, a detailed account is provided of how group theory has been applied across computational structural biology to analyze the conformational shape and motion of macromolecules and complexes. PMID:20827378
Non-rigid molecular group theory and its applications
Balasubramanian, K.
1982-06-01
The use of generalized wreath product groups as representations of symmetry groups of nonrigid molecules is considered. Generating function techniques are outlined for nuclear spin statistics and character tables of the symmetry groups of nonrigid molecules. Several applications of nonrigid molecular group theory to NMR spectroscopy, rovibronic splitting and nuclear spin statistics of nonrigid molecules, molecular beam deflection and electric resonance experiments of weakly bound Van der Waal complexes, isomerization processes, configuration interaction calculations and the symmetry of crystals with structural distortions are described. 81 references.
Quadratic α‧-corrections to heterotic double field theory
NASA Astrophysics Data System (ADS)
Lee, Kanghoon
2015-10-01
We investigate α‧-corrections of heterotic double field theory up to quadratic order in the language of supersymmetric O (D, D + dim G) gauged double field theory. After introducing double-vielbein formalism with a parametrization which reproduces heterotic supergravity, we show that supersymmetry for heterotic double field theory up to leading order α‧-correction is obtained from supersymmetric gauged double field theory. We discuss the necessary modifications of the symmetries defined in supersymmetric gauged double field theory. Further, we construct supersymmetric completion at quadratic order in α‧.
Machine Learning for Dynamical Mean Field Theory
NASA Astrophysics Data System (ADS)
Arsenault, Louis-Francois; Lopez-Bezanilla, Alejandro; von Lilienfeld, O. Anatole; Littlewood, P. B.; Millis, Andy
2014-03-01
Machine Learning (ML), an approach that infers new results from accumulated knowledge, is in use for a variety of tasks ranging from face and voice recognition to internet searching and has recently been gaining increasing importance in chemistry and physics. In this talk, we investigate the possibility of using ML to solve the equations of dynamical mean field theory which otherwise requires the (numerically very expensive) solution of a quantum impurity model. Our ML scheme requires the relation between two functions: the hybridization function describing the bare (local) electronic structure of a material and the self-energy describing the many body physics. We discuss the parameterization of the two functions for the exact diagonalization solver and present examples, beginning with the Anderson Impurity model with a fixed bath density of states, demonstrating the advantages and the pitfalls of the method. DOE contract DE-AC02-06CH11357.
Takiff superalgebras and conformal field theory
NASA Astrophysics Data System (ADS)
Babichenko, Andrei; Ridout, David
2013-03-01
A class of non-semisimple extensions of Lie superalgebras is studied. They are obtained by adjoining to the superalgebra its adjoint representation as an Abelian ideal. When the superalgebra is of affine Kac-Moody type, a generalization of Sugawara’s construction is shown to give rise to a copy of the Virasoro algebra and so, presumably, to a conformal field theory. Evidence for this is detailed for the extension of the affinization of the superalgebra \\mathfrak {gl} ( 1 \\vert 1): its highest weight irreducible modules are classified using spectral flow, the irreducible supercharacters are computed and a continuum version of the Verlinde formula is verified to give non-negative integer structure coefficients. Interpreting these coefficients as those of the Grothendieck ring of fusion, partial results on the true fusion ring and its indecomposable structures are deduced.
Generalized Gibbs ensembles for quantum field theories
NASA Astrophysics Data System (ADS)
Essler, F. H. L.; Mussardo, G.; Panfil, M.
2015-05-01
We consider the nonequilibrium dynamics in quantum field theories (QFTs). After being prepared in a density matrix that is not an eigenstate of the Hamiltonian, such systems are expected to relax locally to a stationary state. In the presence of local conservation laws, these stationary states are believed to be described by appropriate generalized Gibbs ensembles. Here we demonstrate that in order to obtain a correct description of the stationary state, it is necessary to take into account conservation laws that are not (ultra)local in the usual sense of QFTs, but fulfill a significantly weaker form of locality. We discuss the implications of our results for integrable QFTs in one spatial dimension.
Effective field theory analysis of Higgs naturalness
Bar-Shalom, Shaouly; Soni, Amarjit; Wudka, Jose
2015-07-20
Assuming the presence of physics beyond the Standard Model ( SM) with a characteristic scale M ~ O (10) TeV, we investigate the naturalness of the Higgs sector at scales below M using an effective field theory (EFT) approach. We obtain the leading 1 -loop EFT contributions to the Higgs mass with a Wilsonian-like hard cutoff, and determine t he constraints on the corresponding operator coefficients for these effects to alleviate the little hierarchy problem up to the scale of the effective action Λ < M , a condition we denote by “EFT-naturalness”. We also determine the types of physics that can lead to EFT-naturalness and show that these types of new physics are best probed in vector-boson and multiple-Higgs production. The current experimental constraints on these coefficients are also discussed.
Matrix product states for gauge field theories.
Buyens, Boye; Haegeman, Jutho; Van Acoleyen, Karel; Verschelde, Henri; Verstraete, Frank
2014-08-29
The matrix product state formalism is used to simulate Hamiltonian lattice gauge theories. To this end, we define matrix product state manifolds which are manifestly gauge invariant. As an application, we study (1+1)-dimensional one flavor quantum electrodynamics, also known as the massive Schwinger model, and are able to determine very accurately the ground-state properties and elementary one-particle excitations in the continuum limit. In particular, a novel particle excitation in the form of a heavy vector boson is uncovered, compatible with the strong coupling expansion in the continuum. We also study full quantum nonequilibrium dynamics by simulating the real-time evolution of the system induced by a quench in the form of a uniform background electric field. PMID:25215973
The $\\hbar$ Expansion in Quantum Field Theory
Brodsky, Stanley J.; Hoyer, Paul; /Southern Denmark U., CP3-Origins /Helsinki U. /Helsinki Inst. of Phys.
2010-10-27
We show how expansions in powers of Planck's constant {h_bar} = h = 2{pi} can give new insights into perturbative and nonperturbative properties of quantum field theories. Since {h_bar} is a fundamental parameter, exact Lorentz invariance and gauge invariance are maintained at each order of the expansion. The physics of the {h_bar} expansion depends on the scheme; i.e., different expansions are obtained depending on which quantities (momenta, couplings and masses) are assumed to be independent of {h_bar}. We show that if the coupling and mass parameters appearing in the Lagrangian density are taken to be independent of {h_bar}, then each loop in perturbation theory brings a factor of {h_bar}. In the case of quantum electrodynamics, this scheme implies that the classical charge e, as well as the fine structure constant are linear in {h_bar}. The connection between the number of loops and factors of {h_bar} is more subtle for bound states since the binding energies and bound-state momenta themselves scale with {h_bar}. The {h_bar} expansion allows one to identify equal-time relativistic bound states in QED and QCD which are of lowest order in {h_bar} and transform dynamically under Lorentz boosts. The possibility to use retarded propagators at the Born level gives valence-like wave-functions which implicitly describe the sea constituents of the bound states normally present in its Fock state representation.
Non-Abelian gauge field theory in scale relativity
Nottale, Laurent; Celerier, Marie-Noeelle; Lehner, Thierry
2006-03-15
Gauge field theory is developed in the framework of scale relativity. In this theory, space-time is described as a nondifferentiable continuum, which implies it is fractal, i.e., explicitly dependent on internal scale variables. Owing to the principle of relativity that has been extended to scales, these scale variables can themselves become functions of the space-time coordinates. Therefore, a coupling is expected between displacements in the fractal space-time and the transformations of these scale variables. In previous works, an Abelian gauge theory (electromagnetism) has been derived as a consequence of this coupling for global dilations and/or contractions. We consider here more general transformations of the scale variables by taking into account separate dilations for each of them, which yield non-Abelian gauge theories. We identify these transformations with the usual gauge transformations. The gauge fields naturally appear as a new geometric contribution to the total variation of the action involving these scale variables, while the gauge charges emerge as the generators of the scale transformation group. A generalized action is identified with the scale-relativistic invariant. The gauge charges are the conservative quantities, conjugates of the scale variables through the action, which find their origin in the symmetries of the ''scale-space.'' We thus found in a geometric way and recover the expression for the covariant derivative of gauge theory. Adding the requirement that under the scale transformations the fermion multiplets and the boson fields transform such that the derived Lagrangian remains invariant, we obtain gauge theories as a consequence of scale symmetries issued from a geometric space-time description.
Euler-Poincare reduction for discrete field theories
Vankerschaver, Joris
2007-03-15
In this note, we develop a theory of Euler-Poincare reduction for discrete Lagrangian field theories. We introduce the concept of Euler-Poincare equations for discrete field theories, as well as a natural extension of the Moser-Veselov scheme, and show that both are equivalent. The resulting discrete field equations are interpreted in terms of discrete differential geometry. An application to the theory of discrete harmonic mappings is also briefly discussed.
Male Reference Group Identity Dependence: A Theory of Male Identity.
ERIC Educational Resources Information Center
Wade, Jay C.
1998-01-01
Presents a theory of male identity developed to address the question of why men vary in their masculinity ideology and in their conformity to standards of masculinity. An overview of relevant masculinity research, theoretical foundations for the construct of reference group identity dependence, theoretical postulates, associated behavioral, and…
Super-Galilei invariant field theories in 2+1 dimensions
Bergman, O.; Thorn, C.B.
1995-12-31
The authors extend the Galilei group of space-time transformations by gradation, construct interacting field-theoretic representations of this algebra, and show that non-relativistic Super-Chern-Simons theory is a special case. They also study the generalization to matrix valued fields, which are relevant to the formulation of superstring theory as a 1/N{sub c} expansion of a field theory. The authors find that in the matrix case, the field theory is much more restricted by the supersymmetry.
Topological field theory of dynamical systems
Ovchinnikov, Igor V.
2012-09-15
Here, it is shown that the path-integral representation of any stochastic or deterministic continuous-time dynamical model is a cohomological or Witten-type topological field theory, i.e., a model with global topological supersymmetry (Q-symmetry). As many other supersymmetries, Q-symmetry must be perturbatively stable due to what is generically known as non-renormalization theorems. As a result, all (equilibrium) dynamical models are divided into three major categories: Markovian models with unbroken Q-symmetry, chaotic models with Q-symmetry spontaneously broken on the mean-field level by, e.g., fractal invariant sets (e.g., strange attractors), and intermittent or self-organized critical (SOC) models with Q-symmetry dynamically broken by the condensation of instanton-antiinstanton configurations (earthquakes, avalanches, etc.) SOC is a full-dimensional phase separating chaos and Markovian dynamics. In the deterministic limit, however, antiinstantons disappear and SOC collapses into the 'edge of chaos.' Goldstone theorem stands behind spatio-temporal self-similarity of Q-broken phases known under such names as algebraic statistics of avalanches, 1/f noise, sensitivity to initial conditions, etc. Other fundamental differences of Q-broken phases is that they can be effectively viewed as quantum dynamics and that they must also have time-reversal symmetry spontaneously broken. Q-symmetry breaking in non-equilibrium situations (quenches, Barkhausen effect, etc.) is also briefly discussed.
Topological and differential geometrical gauge field theory
NASA Astrophysics Data System (ADS)
Saaty, Joseph
Recent Quantum Field Theory books have defined the topological charge (Q) in terms of the winding number (N). Contrary to this definition, my proof defines Q in terms of the quantum number (n). Defining Q in terms of n, instead of in terms of N, enables me to determine a precise value for Q. The solutions of all kinds of homotopy classification are referred to as instanton solutions, hence the terms homotopy classification and instanton solution will be used interchangeably. My proof replaces the use of these techniques with the use of the Dirac quantization condition, the covariant Dirac's equation, and the covariant Maxwell's equation. Unlike the earlier approaches, my proof accounts for the concept of the spin quantum number and the concept of time. Using the three methods noted above, my proof yields results not obtained by earlier methods. I have dealt similarly with the Pontryagin Index. I have used the Covariant Electrodynamics, in place of homotopy classification techniques, to create for the Pontryagin Index a proof that is alternative to the one cited in recent literature. The homotopy classification techniques gives an expression that excludes the fact that particles have spin quantum number. Therefore, the homotopy classification techniques does not really describe what the topological charge is in reality. I did derive an expression which does include the spin quantum numbers for particles and this has not been done before. Therefore, this will give a better idea for theoretical physicists about the nature of the topological charge. Contribution to knowledge includes creativity. I created an alternative method to the instanton solution for deriving an expression for the topological charge and this method led to new discoveries as a contribution to knowledge in which I found that topological charge for fermions cannot be quantized (to be quantized means to take discrete values only in integer steps), whereas the instanton solution cannot distinguish
Focus Group Effects on Field Practicum Preferences
ERIC Educational Resources Information Center
Sandel, Mark H.; Cohen, Harriet L.; Thomas, Cecilia L.; Barton, Thomas R.
2006-01-01
During the coming years the need for professionals to work with the nation's elders will increase several fold. This will place a great responsibility on university educational programs to prepare enough qualified future professionals to work in the greatly expanding field of gerontology. Prior research has identified several nonacademic and…
On the standard model group in F-theory
NASA Astrophysics Data System (ADS)
Choi, Kang-Sin
2014-06-01
We analyze the standard model gauge group constructed in F-theory. The non-Abelian part is described by a surface singularity of Kodaira type. Blow-up analysis shows that the non-Abelian part is distinguished from the naïve product of and , but that it should be a rank three group along the chain of groups, because it has non-generic gauge symmetry enhancement structure responsible for desirable matter curves. The Abelian part is constructed from a globally valid two-form with the desired gauge quantum numbers, using a similar method to the decomposition (factorization) method of the spectral cover. This technique makes use of an extra section in the elliptic fiber of the Calabi-Yau manifold, on which F-theory is compactified. Conventional gauge coupling unification of is achieved, without requiring a threshold correction from the flux along the hypercharge direction.
Anomalies in non-polynomial closed string field theory
NASA Astrophysics Data System (ADS)
Kaku, Michio
1990-11-01
The complete classical action for the non-polynomial closed string field theory was written down last year by the author and the Kyoto group. It successfully reproduces all closed string tree diagrams, but fails to reproduce modular invariant loop amplitudes. In this paper we show that the classical action is also riddled with gauge anomalies. Thus, the classical action is not really gauge invariant and fails as a quantum theory. The presence of gauge anomalies and the violation of modular invariance appear to be a disaster for the theory. Actually, this is a blessing in disguise. We show that by adding new non-polynomial terms to the action, we can simultaneously eliminate both the gauge anomalies and the modular-violating loop diagrams. We show this explicitly at the one loop level and also for an infinite class of p-puncture, genus- g amplitudes, making use of a series of non-trivial identities. The theory is thus an acceptable quantum theory. We comment on the origin of this strange link between local gauge anomalies and global modular invariance.
Renormalization Group Theory of Bolgiano Scaling in Boussinesq Turbulence
NASA Technical Reports Server (NTRS)
Rubinstein, Robert
1994-01-01
Bolgiano scaling in Boussinesq turbulence is analyzed using the Yakhot-Orszag renormalization group. For this purpose, an isotropic model is introduced. Scaling exponents are calculated by forcing the temperature equation so that the temperature variance flux is constant in the inertial range. Universal amplitudes associated with the scaling laws are computed by expanding about a logarithmic theory. Connections between this formalism and the direct interaction approximation are discussed. It is suggested that the Yakhot-Orszag theory yields a lowest order approximate solution of a regularized direct interaction approximation which can be corrected by a simple iterative procedure.
Geometric and Topological Methods for Quantum Field Theory
NASA Astrophysics Data System (ADS)
Ocampo, Hernan; Pariguan, Eddy; Paycha, Sylvie
2010-04-01
Introduction; 1. The impact of QFT on low-dimensional topology Paul Kirk; 2. Differential equations aspects of quantum cohomology Martin A. Guest; 3. Index theory and groupoids Claire Debord and Jean-Marie Lescure; 4. Renormalization Hopf algebras and combinatorial groups Alessandra Frabetti; 5. BRS invariance for massive boson fields José M. Gracia-Bondía; 6. Large N field theories and geometry David Berenstein; 7. Functional renormalization group equations, asymptotic safety, and quantum Einstein gravity Martin Reuter and Frank Saueressig; 8. When is a differentiable manifold the boundary of an orbifold? Andrés Angel; 9. Canonical group quantization, rotation generators and quantum indistinguishability Carlos Benavides and Andrés Reyes-Lega; 10. Conserved currents in Kähler manifolds Jaime R. Camacaro and Juan Carlos Moreno; 11. A symmetrized canonical determinant on odd-class pseudodifferential operators Marie-Françoise Ouedraogo; 12. Some remarks about cosymplectic metrics on maximal flag manifolds Marlio Paredes and Sofia Pinzón; 13. Heisenberg modules over real multiplication noncommutative tori and related algebraic structures Jorge Plazas; Index.
Gravitational consequences of modern field theories
NASA Technical Reports Server (NTRS)
Horowitz, Gary T.
1989-01-01
Some gravitational consequences of certain extensions of Einstein's general theory of relativity are discussed. These theories are not alternative theories of gravity in the usual sense. It is assumed that general relativity is the appropriate description of all gravitational phenomena which were observed to date.
Double field theory and mathcal{N} = {4} gauged supergravity
NASA Astrophysics Data System (ADS)
Geissbühler, David
2011-11-01
Double Field Theory describes the NS-NS sector of string theory and lives on a doubled spacetime. The theory has a local gauge symmetry generated by a generalization of the Lie derivative for doubled coordinates. For the action to be invariant under this symmetry, a differential constraint is imposed on the fields and gauge parameters, reducing their possible dependence in the doubled coordinates. We perform a Scherk-Schwarz reduction of Double Field Theory, yielding electric gaugings of half-maximal supergravity in four dimensions when integrability conditions are assumed. The residual symmetries of the compactified theory are mapped with the symmetries of the effective theory and the differential constraints of Double Field Theory are compared with the algebraic conditions on the embedding tensor. It is found that only a weaker form of the differential constraint has to be imposed on background fields to ensure the local gauge symmetry of the reduced action.
Superconformal field theory and Jack superpolynomials
NASA Astrophysics Data System (ADS)
Desrosiers, Patrick; Lapointe, Luc; Mathieu, Pierre
2012-09-01
We uncover a deep connection between the {N} = {1} superconformal field theory in 2 D and eigenfunctions of the supersymmetric Sutherland model known as Jack super-polynomials (sJacks). Specifically, the singular vector at level rs/2 of the Kac module labeled by the two integers r and s are given explicitly as a sum of sJacks whose indexing diagrams are contained in a rectangle with r columns and s rows. As a second compelling evidence for the distinguished status of the sJack-basis in SCFT, we find that the degenerate Whittaker vectors (Gaiotto states) can be expressed as a remarkably simple linear combination of sJacks. As a consequence, we are able to reformulate the supersymmetric version of the (degenerate) AGT conjecture in terms of the combinatorics of sJacks. The closed-form formulas for the singular vectors and the degenerate Whittaker vectors, although only conjectured in general, have been heavily tested (in some cases, up to level 33/2). Both the Neveu-Schwarz and Ramond sectors are treated.
Gravitational Descendants in Symplectic Field Theory
NASA Astrophysics Data System (ADS)
Fabert, Oliver
2011-02-01
It was pointed out by Y. Eliashberg in his ICM 2006 plenary talk that the rich algebraic formalism of symplectic field theory leads to a natural appearance of quantum and classical integrable systems, at least in the case when the contact manifold is the prequantization space of a symplectic manifold. In this paper we generalize the definition of gravitational descendants in SFT from circle bundles in the Morse-Bott case to general contact manifolds. After we have shown using the ideas in Okounkov and Pandharipande (Ann Math 163(2):517-560, 2006) that for the basic examples of holomorphic curves in SFT, that is, branched covers of cylinders over closed Reeb orbits, the gravitational descendants have a geometric interpretation in terms of branching conditions, we follow the ideas in Cieliebak and Latschev (
Quantifying truncation errors in effective field theory
NASA Astrophysics Data System (ADS)
Furnstahl, R. J.; Klco, N.; Phillips, D. R.; Wesolowski, S.
2015-08-01
Bayesian procedures designed to quantify truncation errors in perturbative calculations of quantum chromodynamics observables are adapted to expansions in effective field theory (EFT). In the Bayesian approach, such truncation errors are derived from degree-of-belief (DOB) intervals for EFT predictions. Computation of these intervals requires specification of prior probability distributions ("priors") for the expansion coefficients. By encoding expectations about the naturalness of these coefficients, this framework provides a statistical interpretation of the standard EFT procedure where truncation errors are estimated using the order-by-order convergence of the expansion. It also permits exploration of the ways in which such error bars are, and are not, sensitive to assumptions about EFT-coefficient naturalness. We first demonstrate the calculation of Bayesian probability distributions for the EFT truncation error in some representative examples and then focus on the application of chiral EFT to neutron-proton scattering. Epelbaum, Krebs, and Meißner recently articulated explicit rules for estimating truncation errors in such EFT calculations of few-nucleon-system properties. We find that their basic procedure emerges generically from one class of naturalness priors considered and that all such priors result in consistent quantitative predictions for 68% DOB intervals. We then explore several methods by which the convergence properties of the EFT for a set of observables may be used to check the statistical consistency of the EFT expansion parameter.
Quantifying truncation errors in effective field theory
NASA Astrophysics Data System (ADS)
Furnstahl, R. J.; Klco, N.; Phillips, D. R.; Wesolowski, S.
2015-10-01
Bayesian procedures designed to quantify truncation errors in perturbative calculations of QCD observables are adapted to expansions in effective field theory (EFT). In the Bayesian approach, such truncation errors are derived from degree-of-belief (DOB) intervals for EFT predictions. Computation of these intervals requires specification of prior probability distributions (``priors'') for the expansion coefficients. By encoding expectations about the naturalness of these coefficients, this framework provides a statistical interpretation of the standard EFT procedure where truncation errors are estimated using the order-by-order convergence of the expansion. It also permits exploration of the ways in which such error bars are, and are not, sensitive to assumptions about EFT-coefficient naturalness. We demonstrate the calculation of Bayesian DOB intervals for the EFT truncation error in some representative cases and explore several methods by which the convergence properties of the EFT for a set of observables may be used to check the statistical consistency of the EFT expansion parameter. Supported in part by the NSF and the DOE.
The Family FIRO Model: The Integration of Group Theory and Family Theory.
ERIC Educational Resources Information Center
Colangelo, Nicholas; Doherty, William J.
1988-01-01
Presents the Family Fundamental Interpersonal Relations Orientation (Family FIRO) Model, an integration of small-group theory and family therapy. The model is offered as a framework for organizing family issues. Discusses three fundamental issues of human relatedness and their applicability to group dynamics. (Author/NB)
Heterotic α'-corrections in Double Field Theory
NASA Astrophysics Data System (ADS)
Bedoya, Oscar A.; Marqués, Diego; Núñez, Carmen
2014-12-01
We extend the generalized flux formulation of Double Field Theory to include all the first order bosonic contributions to the α' expansion of the heterotic string low energy effective theory. The generalized tangent space and duality group are enhanced by α' corrections, and the gauge symmetries are generated by the usual (gauged) generalized Lie derivative in the extended space. The generalized frame receives derivative corrections through the spin connection with torsion, which is incorporated as a new degree of freedom in the extended bein. We compute the generalized fluxes and find the Riemann curvature tensor with torsion as one of their components. All the four-derivative terms of the action, Bianchi identities and equations of motion are reproduced. Using this formalism, we obtain the first order α' corrections to the heterotic Buscher rules. The relation of our results to alternative formulations in the literature is discussed and future research directions are outlined.
Translational symmetry breaking in field theories and the cosmological constant
NASA Astrophysics Data System (ADS)
Evans, Nick; Morris, Tim R.; Scott, Marc
2016-01-01
We argue, at a very basic effective field theory level, that higher dimension operators in scalar theories that break symmetries at scales close to their ultraviolet completion cutoff include terms that favor the breaking of translation (Lorentz) invariance, potentially resulting in striped, checkerboard or general crystal-like phases. Such descriptions can be thought of as the effective low energy description of QCD-like gauge theories near their strong coupling scale where terms involving higher dimension operators are generated. Our low energy theory consists of scalar fields describing operators such as q ¯q and q ¯F(2 n )q . Such scalars can have kinetic mixing terms that generate effective momentum dependent contributions to the mass matrix. We show that these can destabilize the translationally invariant vacuum. It is possible that in some real gauge theory such operators could become sufficiently dominant to realize such phases, and it would be interesting to look for them in lattice simulations. We present a holographic model of the same phenomena which includes renormalization group running. A key phenomenological motive to look at such states is recent work that shows that the nonlinear response in R2 gravity to such short-range fluctuations can mimic a cosmological constant. Intriguingly in a cosmology with such a Starobinsky inflation term, to generate the observed value of the present day acceleration would require stripes at the electroweak scale. Unfortunately, low energy phenomenological constraints on Lorentz violation in the electron-photon system appear to strongly rule out any such possibility outside of a disconnected dark sector.
NASA Astrophysics Data System (ADS)
Zatloukal, Václav
2016-04-01
Classical field theory is considered as a theory of unparametrized surfaces embedded in a configuration space, which accommodates, in a symmetric way, spacetime positions and field values. Dynamics is defined by a (Hamiltonian) constraint between multivector-valued generalized momenta, and points in the configuration space. Starting from a variational principle, we derive local equations of motion, that is, differential equations that determine classical surfaces and momenta. A local Hamilton-Jacobi equation applicable in the field theory then follows readily. The general method is illustrated with three examples: non-relativistic Hamiltonian mechanics, De Donder-Weyl scalar field theory, and string theory.
Group Decisions in Biodiversity Conservation: Implications from Game Theory
Frank, David M.; Sarkar, Sahotra
2010-01-01
Background Decision analysis and game theory [1], [2] have proved useful tools in various biodiversity conservation planning and modeling contexts [3]–[5]. This paper shows how game theory may be used to inform group decisions in biodiversity conservation scenarios by modeling conflicts between stakeholders to identify Pareto–inefficient Nash equilibria. These are cases in which each agent pursuing individual self–interest leads to a worse outcome for all, relative to other feasible outcomes. Three case studies from biodiversity conservation contexts showing this feature are modeled to demonstrate how game–theoretical representation can inform group decision-making. Methodology and Principal Findings The mathematical theory of games is used to model three biodiversity conservation scenarios with Pareto–inefficient Nash equilibria: (i) a two–agent case involving wild dogs in South Africa; (ii) a three–agent raptor and grouse conservation scenario from the United Kingdom; and (iii) an n–agent fish and coral conservation scenario from the Philippines. In each case there is reason to believe that traditional mechanism–design solutions that appeal to material incentives may be inadequate, and the game–theoretical analysis recommends a resumption of further deliberation between agents and the initiation of trust—and confidence—building measures. Conclusions and Significance Game theory can and should be used as a normative tool in biodiversity conservation contexts: identifying scenarios with Pareto–inefficient Nash equilibria enables constructive action in order to achieve (closer to) optimal conservation outcomes, whether by policy solutions based on mechanism design or otherwise. However, there is mounting evidence [6] that formal mechanism–design solutions may backfire in certain cases. Such scenarios demand a return to group deliberation and the creation of reciprocal relationships of trust. PMID:20523732
Magnetism and rotation in relativistic field theory
NASA Astrophysics Data System (ADS)
Mameda, Kazuya; Yamamoto, Arata
2016-09-01
We investigate the analogy between magnetism and rotation in relativistic theory. In nonrelativistic theory, the exact correspondence between magnetism and rotation is established in the presence of an external trapping potential. Based on this, we analyze relativistic rotation under external trapping potentials. A Landau-like quantization is obtained by considering an energy-dependent potential.
The State of the Field: Interdisciplinary Theory
ERIC Educational Resources Information Center
Newell, William H.
2013-01-01
This chronological overview of the development of interdisciplinary theory starts with the pre-cursors of theory: the development and elaboration of the definition of interdisciplinary studies, influential but problematic images of interdisciplinary studies proposed by Donald Campbell and Erich Jantsch, and best practices in interdisciplinary…
Simple space-time symmetries: Generalizing conformal field theory
Mack, Gerhard; Riese, Mathias de
2007-05-15
We study simple space-time symmetry groups G which act on a space-time manifold M=G/H which admits a G-invariant global causal structure. We classify pairs (G,M) which share the following additional properties of conformal field theory. (1) The stability subgroup H of o set-membership sign M is the identity component of a parabolic subgroup of G, implying factorization H=MAN{sup -}, where M generalizes Lorentz transformations, A dilatations, and N{sup -} special conformal transformations. (2) Special conformal transformations {xi} set-membership sign N{sup -} act trivially on tangent vectors v set-membership sign T{sub o}M. The allowed simple Lie groups G are the universal coverings of SU(m,m),SO(2,D),Sp(l,R),SO*(4n), and E{sub 7(-25)} and H are particular maximal parabolic subgroups. They coincide with the groups of fractional linear transformations of Euclidean Jordan algebras whose use as generalizations of Minkowski space-time was advocated by Guenaydin [Mod. Phys. Lett. A 8, 1407 (1993)]. All these groups G admit positive energy representations. It will also be shown that the classical conformal groups SO(2,D) are the only allowed groups which possess an automorphism with properties appropriate for a time reflection.
Field theory on R× S 3 topology. VI: Gravitation
NASA Astrophysics Data System (ADS)
Carmeli, M.; Malin, S.
1987-04-01
We extend to curved space-time the field theory on R×S3 topology in which field equations were obtained for scalar particles, spin one-half particles, the electromagnetic field of magnetic moments, an SU2 gauge theory, and a Schrödinger-type equation, as compared to ordinary field equations that are formulated on a Minkowskian metric. The theory obtained is an angular-momentum representation of gravitation. Gravitational field equations are presented and compared to the Einstein field equations, and the mathematical and physical similarity and differences between them are pointed out. The problem of motion is discussed, and the equations of motion of a rigid body are developed and given explicitly. One result which is worth emphazing is that while general relativity theory yields Newton's law of motion in the lowest approximation, our theory gives Euler's equations of motion for a rigid body in its lowest approximation.
Phase cell cluster expansion for Euclidean field theories
Battle, G.A. III; Federbush, P.
1982-08-01
We adapt the cluster expansion first used to treat infrared problems for lattice models (a mass zero cluster expansion) to the usual field theory situation. The field is expanded in terms of spectral block spin functions and the cluster expansion given in terms of the expansion coefficients (phase cell variables); the other cluster expansion expresses correlation functions in terms of contributions from finite coupled subsets of these variables. Most of the present work is carried through in d space time dimensions (for phi/sup 4//sub 2/ the details of the cluster expansion are pursued and convergence is proven). Thus most of the results in this present work will apply to a treatment of phi/sup 4//sub 3/ to which we hope to return in a succeeding paper. Of particular interest in this paper is a substitute for the stability of the vaccum bound appropriate to this cluster expansion (for d = 2 and d = 3), and the new method for performing estimates with tree graphs. The phase cell cluster expansions have the renormalization group incorporated intimately into their structure. We hope they will be useful ultimately in treating four dimensional field theories.
Exploring Group Cohesion in a Higher Education Field Experience
ERIC Educational Resources Information Center
Malcarne, Brian Keith
2012-01-01
The purpose of this study was to gain understanding into the experience of group cohesion for university students participating in an academic field experience. A mixed methods approach was used following a two-phase, sequential research design to help provide a more complete explanation of how group cohesion was impacted by the field experience.…
Challenging Gender Stereotypes: Theory of Mind and Peer Group Dynamics
Mulvey, Kelly Lynn; Rizzo, Michael T.; Killen, Melanie
2016-01-01
To investigate the social cognitive skills related to challenging gender stereotypes, children (N = 61, 3-6 years) evaluated a peer who challenged gender stereotypic norms held by the peer’s group. Participants with false belief theory of mind (FB ToM) competence were more likely than participants who did not have FB ToM to expect a peer to challenge the group’s stereotypes and propose that the group engage in a non-stereotypic activity. Further, participants with FB ToM rated challenging the peer group more positively. Participants without FB ToM did not differentiate between their own and the group’s evaluation of challenges to the group’s stereotypic norms, but those with ToM competence asserted that they would be more supportive of challenging the group norm than would the peer group. Results reveal the importance of social-cognitive competencies for recognizing the legitimacy of challenging stereotypes, and for understanding one’s own and other group perspectives. PMID:26395753
Infrared Yang-Mills theory: A renormalization group perspective
NASA Astrophysics Data System (ADS)
Weber, Axel; Dall’Olio, Pietro; Astorga, Francisco
2016-05-01
We describe a technically very simple analytical approach to the deep infrared regime of Yang-Mills theory in the Landau gauge via Callan-Symanzik renormalization group equations in an epsilon expansion. This approach recovers all the solutions for the infrared gluon and ghost propagators previously found by solving the Dyson-Schwinger equations of the theory and singles out the solution with decoupling behavior, confirmed by lattice calculations, as the only one corresponding to an infrared attractive fixed point (for space-time dimensions above two). For the case of four dimensions, we describe the crossover of the system from the ultraviolet to the infrared fixed point and determine the complete momentum dependence of the propagators. The results for different renormalization schemes are compared to the lattice data.
Some aspects of the theory of quantum groups
NASA Astrophysics Data System (ADS)
Demidov, E. E.
1993-12-01
CONTENTSIntroductionChapter I. Basic constructions § 1. Definition of a Hopf algebra § 2. Two constructions of quantum semigroups § 3. Universal coacting and R-matrix algebras § 4. The quantum determinant and antipode § 5. The dimension of quantum semigroupsChapter II. Representation theory § 6. Basic concepts of representation theory § 7. The quantum flag space of \\operatorname{GL}_{P, \\mathcal Q, c}(n) § 8. The Schur algebra and complete reducibility § 9. Representations of \\operatorname{SL}_J(2) §10. The Frobenius morphismChapter III. Non-commutative differential calculus §11. The non-commutative de Rham complex of an n-dimensional vector space §12. Quantum Weyl algebras §13. The de Rham complex of a quantum groupReferences
Modern Quantum Field Theory II - Proceeeings of the International Colloquium
NASA Astrophysics Data System (ADS)
Das, S. R.; Mandal, G.; Mukhi, S.; Wadia, S. R.
1995-08-01
The Table of Contents for the book is as follows: * Foreword * 1. Black Holes and Quantum Gravity * Quantum Black Holes and the Problem of Time * Black Hole Entropy and the Semiclassical Approximation * Entropy and Information Loss in Two Dimensions * Strings on a Cone and Black Hole Entropy (Abstract) * Boundary Dynamics, Black Holes and Spacetime Fluctuations in Dilation Gravity (Abstract) * Pair Creation of Black Holes (Abstract) * A Brief View of 2-Dim. String Theory and Black Holes (Abstract) * 2. String Theory * Non-Abelian Duality in WZW Models * Operators and Correlation Functions in c ≤ 1 String Theory * New Symmetries in String Theory * A Look at the Discretized Superstring Using Random Matrices * The Nested BRST Structure of Wn-Symmetries * Landau-Ginzburg Model for a Critical Topological String (Abstract) * On the Geometry of Wn Gravity (Abstract) * O(d, d) Tranformations, Marginal Deformations and the Coset Construction in WZNW Models (Abstract) * Nonperturbative Effects and Multicritical Behaviour of c = 1 Matrix Model (Abstract) * Singular Limits and String Solutions (Abstract) * BV Algebra on the Moduli Spaces of Riemann Surfaces and String Field Theory (Abstract) * 3. Condensed Matter and Statistical Mechanics * Stochastic Dynamics in a Deposition-Evaporation Model on a Line * Models with Inverse-Square Interactions: Conjectured Dynamical Correlation Functions of the Calogero-Sutherland Model at Rational Couplings * Turbulence and Generic Scale Invariance * Singular Perturbation Approach to Phase Ordering Dynamics * Kinetics of Diffusion-Controlled and Ballistically-Controlled Reactions * Field Theory of a Frustrated Heisenberg Spin Chain * FQHE Physics in Relativistic Field Theories * Importance of Initial Conditions in Determining the Dynamical Class of Cellular Automata (Abstract) * Do Hard-Core Bosons Exhibit Quantum Hall Effect? (Abstract) * Hysteresis in Ferromagnets * 4. Fundamental Aspects of Quantum Mechanics and Quantum Field Theory
Dynamics of polymers: A mean-field theory
Fredrickson, Glenn H.; Orland, Henri
2014-02-28
We derive a general mean-field theory of inhomogeneous polymer dynamics; a theory whose form has been speculated and widely applied, but not heretofore derived. Our approach involves a functional integral representation of a Martin-Siggia-Rose (MSR) type description of the exact many-chain dynamics. A saddle point approximation to the generating functional, involving conditions where the MSR action is stationary with respect to a collective density field ρ and a conjugate MSR response field ϕ, produces the desired dynamical mean-field theory. Besides clarifying the proper structure of mean-field theory out of equilibrium, our results have implications for numerical studies of polymer dynamics involving hybrid particle-field simulation techniques such as the single-chain in mean-field method.
Effective field theory of broken spatial diffeomorphisms
Lin, Chunshan; Labun, Lance Z.
2016-03-17
We study the low energy effective theory describing gravity with broken spatial diffeomorphism invariance. In the unitary gauge, the Goldstone bosons associated with broken diffeomorphisms are eaten and the graviton becomes a massive spin-2 particle with 5 well-behaved degrees of freedom. In this gauge, the most general theory is built with the lowest dimension operators invariant under only temporal diffeomorphisms. Imposing the additional shift and SO(3) internal symmetries, we analyze the perturbations on a FRW background. At linear perturbation level, the observables of this theory are characterized by five parameters, including the usual cosmological parameters and one additional coupling constantmore » for the symmetry-breaking scalars. In the de Sitter and Minkowski limit, the three Goldstone bosons are supermassive and can be integrated out, leaving two massive tensor modes as the only propagating degrees of freedom. In conclusion, we discuss several examples relevant to theories of massive gravity.« less
Effective field theory of broken spatial diffeomorphisms
NASA Astrophysics Data System (ADS)
Lin, Chunshan; Labun, Lance Z.
2016-03-01
We study the low energy effective theory describing gravity with broken spatial diffeomorphism invariance. In the unitary gauge, the Goldstone bosons associated with broken diffeomorphisms are eaten and the graviton becomes a massive spin-2 particle with 5 well-behaved degrees of freedom. In this gauge, the most general theory is built with the lowest dimension operators invariant under only temporal diffeomorphisms. Imposing the additional shift and SO(3) internal symmetries, we analyze the perturbations on a FRW background. At linear perturbation level, the observables of this theory are characterized by five parameters, including the usual cosmological parameters and one additional coupling constant for the symmetry-breaking scalars. In the de Sitter and Minkowski limit, the three Goldstone bosons are supermassive and can be integrated out, leaving two massive tensor modes as the only propagating degrees of freedom. We discuss several examples relevant to theories of massive gravity.
Wick rotation for quantum field theories on degenerate Moyal space(-time)
Grosse, Harald; Lechner, Gandalf; Ludwig, Thomas; Verch, Rainer
2013-02-15
In this paper the connection between quantum field theories on flat noncommutative space(-times) in Euclidean and Lorentzian signature is studied for the case that time is still commutative. By making use of the algebraic framework of quantum field theory and an analytic continuation of the symmetry groups which are compatible with the structure of Moyal space, a general correspondence between field theories on Euclidean space satisfying a time zero condition and quantum field theories on Moyal Minkowski space is presented ('Wick rotation'). It is then shown that field theories transferred to Moyal space(-time) by Rieffel deformation and warped convolution fit into this framework, and that the processes of Wick rotation and deformation commute.
Stability in higher-derivative matter fields theories
NASA Astrophysics Data System (ADS)
Tretyakov, Petr V.
2016-09-01
We discuss possible instabilities in higher-derivative matter field theories. These theories have two free parameters β _1 and β _4. By using a dynamical system approach we explicitly demonstrate that for the stability of Minkowski space in an expanding universe we need the condition β _4<0. By using the quantum field theory approach we also find an additional restriction for the parameters, β _1>-1/3β _4, which is needed to avoid a tachyon-like instability.
GravitoMagnetic Field in Tensor-Vector-Scalar Theory
Exirifard, Qasem
2013-04-01
We study the gravitomagnetism in the TeVeS theory. We compute the gravitomagnetic field that a slow moving mass distribution produces in its Newtonian regime. We report that the consistency between the TeVeS gravitomagnetic field and that predicted by the Einstein-Hilbert theory leads to a relation between the vector and scalar coupling constants of the theory. We translate the Lunar Laser Ranging measurement's data into a constraint on the deviation from this relation.
Topological field theory for 2+1 TRI TSC
NASA Astrophysics Data System (ADS)
Gu, Yingfei; Qi, Xiaoliang
2014-03-01
Time-reversal invariant topological superconductors (TRI TSC) are gapped TRI superconductors with topologically robust gapless modes on the boundary. In the work by X. L. Qi et al, [PRB, 87, 134519(2013)], a topological field theory description was proposed for 3+1-dimensional TRI TSC, which contains an axionic coupling between superconducting phase and electromagnetic field. In my talk, I will describe a generalization of this theory to the 2+1 dimensional TRI TSC. The 2+1d topological field theory describes a topological coupling between electromagnetic field, superconducting phase fluctuation and magneto-electric polarization. I will also talk about the corresponding physical consequences.
Mean-field theory for Bose-Hubbard model under a magnetic field
Oktel, M. Oe.; Tanatar, B.; Nita, M.
2007-01-15
We consider the superfluid-insulator transition for cold bosons under an effective magnetic field. We investigate how the applied magnetic field affects the Mott transition within mean-field theory and find that the critical hopping strength (t/U){sub c} increases with the applied field. The increase in the critical hopping follows the bandwidth of the Hofstadter butterfly at the given value of the magnetic field. We also calculate the magnetization and superfluid density within mean-field theory.
Review and application of group theory to molecular systems biology
2011-01-01
In this paper we provide a review of selected mathematical ideas that can help us better understand the boundary between living and non-living systems. We focus on group theory and abstract algebra applied to molecular systems biology. Throughout this paper we briefly describe possible open problems. In connection with the genetic code we propose that it may be possible to use perturbation theory to explore the adjacent possibilities in the 64-dimensional space-time manifold of the evolving genome. With regards to algebraic graph theory, there are several minor open problems we discuss. In relation to network dynamics and groupoid formalism we suggest that the network graph might not be the main focus for understanding the phenotype but rather the phase space of the network dynamics. We show a simple case of a C6 network and its phase space network. We envision that the molecular network of a cell is actually a complex network of hypercycles and feedback circuits that could be better represented in a higher-dimensional space. We conjecture that targeting nodes in the molecular network that have key roles in the phase space, as revealed by analysis of the automorphism decomposition, might be a better way to drug discovery and treatment of cancer. PMID:21696623
Integrable perturbations of conformal field theories and Yetter-Drinfeld modules
Bücher, David; Runkel, Ingo
2014-11-15
In this paper we relate a problem in representation theory — the study of Yetter-Drinfeld modules over certain braided Hopf algebras — to a problem in two-dimensional quantum field theory, namely, the identification of integrable perturbations of a conformal field theory. A prescription that parallels Lusztig's construction allows one to read off the quantum group governing the integrable symmetry. As an example, we illustrate how the quantum group for the loop algebra of sl(2) appears in the integrable structure of the perturbed uncompactified and compactified free boson.
Field Theory Model of the Flyby Anomaly
Lewis, R. A
2009-03-16
Precision tracking of spacecraft on interplanetary missions has turned up several anomalous deviations from predictions of general relativity. The Flyby Anomaly, wherein spacecraft gain or lose energy in an earth-centric frame after an encounter with earth, is clearly associated with the rotation of the earth. The possibility that the missing ingredient is a new type of potential field surrounding the earth is assessed in this write-up. A scalar field with the kinetic energy distribution of the earth as a source is evaluated numerically, with an amplitude parameter adjusted to match the data of Anderson et al.(2008). The new field can be interpreted as a coupling between kinetic energies of objects, a field analogous to fluid mechanics, or a field coupled to acceleration. The potential field violates various aspects of standard physics, such as energy non-conservation.
Universal behavior after a quantum quench in interacting field theories
NASA Astrophysics Data System (ADS)
Mitra, Aditi
The dynamics of an isolated quantum system represented by a field theory with O(N) symmetry, and in d>2 spatial dimensions, is investigated after a quantum quench from a disordered initial state to the critical point. A perturbative renormalization-group approach involving an expansion around d=4 is employed to study the time-evolution, and is supplemented by an exact solution of the Hartree-Fock equations in the large-N limit. The results show that the dynamics is characterized by a prethermal regime controlled by elastic dephasing where excitations propagate ballistically, and a light cone emerges in correlation functions in real space. The memory of the initial state, together with the absence of time-scales at the critical point, gives rise to universal power-law aging which is characterized by a new non-equilibrium short-time exponent. The dynamics of the entanglement following a quench is also explored, and reveals that while the time evolution of the entanglement entropy itself is not much different between a free bosonic theory and an interacting bosonic theory, the low-energy entanglement spectrum on the other hand shows clear signature of the non-equilibrium short-time exponent related to aging. This work was done in collaboration with Y. Lemonik (NYU), M. Tavora (NYU), A. Chiocchetta (SISSA), A. Maraga (SISSA), and A. Gambassi (SISSA). Supported by NSF-DMR 1303177.
Quantum field theory of the Casimir effect for real media
Mostepanenko, V.M.; Trunov, N.N.
1985-11-01
The quantum field theory is developed for the corrections to the Casimir force arising when the field penetrates the material of the plates. A new type of divergence arising from the corresponding modification of the boundary conditions is analyzed. General expressions are obtained for the vacuum energy of the electromagnetic field in the space between nonideal plates, and the actual corrections to the Casimir force are calculated in first-order perturbation theory in the penetration depth.
Open superstring field theory on the restricted Hilbert space
NASA Astrophysics Data System (ADS)
Konopka, Sebastian; Sachs, Ivo
2016-04-01
It appears that the formulation of an action for the Ramond sector of open superstring field theory requires to either restrict the Hilbert space for the Ramond sector or to introduce auxiliary fields with picture -3/2. The purpose of this note is to clarify the relation of the restricted Hilbert space with other approaches and to formulate open superstring field theory entirely in the small Hilbert space.
Quiver theories for moduli spaces of classical group nilpotent orbits
NASA Astrophysics Data System (ADS)
Hanany, Amihay; Kalveks, Rudolph
2016-06-01
We approach the topic of Classical group nilpotent orbits from the perspective of the moduli spaces of quivers, described in terms of Hilbert series and generating functions. We review the established Higgs and Coulomb branch quiver theory constructions for A series nilpotent orbits. We present systematic constructions for BCD series nilpotent orbits on the Higgs branches of quiver theories defined by canonical partitions; this paper collects earlier work into a systematic framework, filling in gaps and providing a complete treatment. We find new Coulomb branch constructions for above minimal nilpotent orbits, including some based upon twisted affine Dynkin diagrams. We also discuss aspects of 3 d mirror symmetry between these Higgs and Coulomb branch constructions and explore dualities and other relationships, such as HyperKähler quotients, between quivers. We analyse all Classical group nilpotent orbit moduli spaces up to rank 4 by giving their unrefined Hilbert series and the Highest Weight Generating functions for their decompositions into characters of irreducible representations and/or Hall Littlewood polynomials.
Quantum revivals in conformal field theories in higher dimensions
NASA Astrophysics Data System (ADS)
Cardy, John
2016-10-01
We investigate the behavior of the return amplitude { F }(t)=| < {{\\Psi }}(0)| {{\\Psi }}(t)> | following a quantum quench in a conformal field theory (CFT) on a compact spatial manifold of dimension d-1 and linear size O(L), from a state | {{\\Psi }}(0)> of extensive energy with short-range correlations. After an initial gaussian decay { F }(t) reaches a plateau value related to the density of available states at the initial energy. However for d=3,4 this value is attained from below after a single oscillation. For a holographic CFT the plateau persists up to times at least O({σ }1/(d-1)L), where σ \\gg 1 is the dimensionless Stefan-Boltzmann constant. On the other hand for a free field theory on manifolds with high symmetry there are typically revivals at times t˜ {{integer}}× L. In particular, on a sphere {S}d-1 of circumference 2π L, there is an action of the modular group on { F }(t) implying structure near all rational values of t/L, similar to what happens for rational CFTs in d=2.
Lorentz symmetry breaking as a quantum field theory regulator
Visser, Matt
2009-07-15
Perturbative expansions of quantum field theories typically lead to ultraviolet (short-distance) divergences requiring regularization and renormalization. Many different regularization techniques have been developed over the years, but most regularizations require severe mutilation of the logical foundations of the theory. In contrast, breaking Lorentz invariance, while it is certainly a radical step, at least does not damage the logical foundations of the theory. I shall explore the features of a Lorentz symmetry breaking regulator in a simple polynomial scalar field theory and discuss its implications. In particular, I shall quantify just 'how much' Lorentz symmetry breaking is required to fully regulate the quantum theory and render it finite. This scalar field theory provides a simple way of understanding many of the key features of Horava's recent article [Phys. Rev. D 79, 084008 (2009)] on 3+1 dimensional quantum gravity.
On the stability of the asymptotically free scalar field theories
Shalaby, A M.
2015-03-30
Asymptotic freedom plays a vital role in our understanding of the theory of particle interactions. To have this property, one has to resort to a Non-abelian gauge theory with the number of colors equal to or greater than three (QCD). However, recent studies have shown that simple scalar field theories can possess this interesting property. These theories have non-Hermitian effective field forms but their classical potentials are bounded from above. In this work, we shall address the stability of the vacua of the bounded from above (−Φ{sup 4+n}) scalar field theories. Moreover, we shall cover the effect of the distribution of the Stokes wedges in the complex Φ-plane on the features of the vacuum condensate within these theories.
Applying Power Theories to Field Settings.
ERIC Educational Resources Information Center
Liss, Lora
To test theories presented in the sociology course "Social Policies and Community Power Structure," a team of undergraduate students and their instructor attended a national professional conference. The following are examples of those concepts the students observed in operation at the conference: Social structure affects social policies; the…
A class of effective field theory models of cosmic acceleration
Bloomfield, Jolyon K.; Flanagan, Éanna É. E-mail: eef3@cornell.edu
2012-10-01
We explore a class of effective field theory models of cosmic acceleration involving a metric and a single scalar field. These models can be obtained by starting with a set of ultralight pseudo-Nambu-Goldstone bosons whose couplings to matter satisfy the weak equivalence principle, assuming that one boson is lighter than all the others, and integrating out the heavier fields. The result is a quintessence model with matter coupling, together with a series of correction terms in the action in a covariant derivative expansion, with specific scalings for the coefficients. After eliminating higher derivative terms and exploiting the field redefinition freedom, we show that the resulting theory contains nine independent free functions of the scalar field when truncated at four derivatives. This is in contrast to the four free functions found in similar theories of single-field inflation, where matter is not present. We discuss several different representations of the theory that can be obtained using the field redefinition freedom. For perturbations to the quintessence field today on subhorizon lengthscales larger than the Compton wavelength of the heavy fields, the theory is weakly coupled and natural in the sense of t'Hooft. The theory admits a regime where the perturbations become modestly nonlinear, but very strong nonlinearities lie outside its domain of validity.
The Theory of Field Parameters for Helmholtz Coil
NASA Astrophysics Data System (ADS)
Wang, Jin; Li, Guofeng; Liang, Ke; Gao, Xianhu
In this paper, the field parameters for the magnetic field of a Helmholtz coil is defined, as predicted by the theory of magnetic multipolar fields. In accordance with Biot-Savart law, eleven series of field parameters for the Helmholtz coil are calculated and the effect of each parameter thoroughly analyzed. This is then shown to provide a theoretical basis for obtaining a uniform magnetic field.
Unambiguous formalism for higher order Lagrangian field theories
NASA Astrophysics Data System (ADS)
Campos, Cédric M.; de León, Manuel; Martín de Diego, David; Vankerschaver, Joris
2009-11-01
The aim of this paper is to propose an unambiguous intrinsic formalism for higher order field theories which avoids the arbitrariness in the generalization of the conventional description of field theories, and implies the existence of different Cartan forms and Legendre transformations. We propose a differential-geometric setting for the dynamics of a higher order field theory, based on the Skinner and Rusk formalism for mechanics. This approach incorporates aspects of both the Lagrangian and the Hamiltonian description, since the field equations are formulated using the Lagrangian on a higher order jet bundle and the canonical multisymplectic form on its affine dual. As both of these objects are uniquely defined, the Skinner-Rusk approach has the advantage that it does not suffer from the arbitrariness in conventional descriptions. The result is that we obtain a unique and global intrinsic version of the Euler-Lagrange equations for higher order field theories. Several examples illustrate our construction.
Quantum Simulation of Quantum Field Theories in Trapped Ions
Casanova, J.; Lamata, L.; Egusquiza, I. L.; Gerritsma, R.; Roos, C. F.; Garcia-Ripoll, J. J.; Solano, E.
2011-12-23
We propose the quantum simulation of fermion and antifermion field modes interacting via a bosonic field mode, and present a possible implementation with two trapped ions. This quantum platform allows for the scalable add up of bosonic and fermionic modes, and represents an avenue towards quantum simulations of quantum field theories in perturbative and nonperturbative regimes.
Killing vector fields and harmonic superfield theories
Groeger, Josua
2014-09-15
The harmonic action functional allows a natural generalisation to semi-Riemannian supergeometry, also referred to as harmonic, which resembles the supersymmetric sigma models studied in high energy physics. We show that Killing vector fields are infinitesimal supersymmetries of this harmonic action and prove three different Noether theorems in this context. En passant, we provide a homogeneous treatment of five characterisations of Killing vector fields on semi-Riemannian supermanifolds, thus filling a gap in the literature.
Theory and Simulation of Field Error Transport.
NASA Astrophysics Data System (ADS)
Dubin, D. H. E.
2007-11-01
The rate at which a plasma escapes across an applied magnetic field B due to symmetry-breaking electric or magnetic ``field errors'' is revisited. Such field errors cause plasma loss (or compression) in stellarators, tokamaks,ootnotetextH.E. Mynick, Ph Plas 13 058102 (2006). and nonneutral plasmas.ootnotetextEggleston, Ph Plas 14 012302 (07); Danielson et al., Ph Plas 13 055706. We study this process using idealized simulations that follow guiding centers in given trap fields, neglecting their collective effect on the evolution, but including collisions. Also, the Fokker-Planck equation describing the particle distribution is solved, and the predicted transport agrees with simulations in every applicable regime. When a field error of the form δφ(r, θ, z ) = ɛ(r) e^i m θ kz is applied to an infinite plasma column, the transport rates fall into the usual banana, plateau and fluid regimes. When the particles are axially confined by applied trap fields, the same three regimes occur. When an added ``squeeze'' potential produces a separatrix in the axial motion, the transport is enhanced, scaling roughly as ( ν/ B )^1/2 δ2̂ when ν< φ. For φ< ν< φB (where φ, ν and φB are the rotation, collision and axial bounce frequencies) there is also a 1/ ν regime similar to that predicted for ripple-enhanced transport.^1
No resonant tunneling in standard scalar quantum field theory
NASA Astrophysics Data System (ADS)
Copeland, Edmund J.; Padilla, Antonio; Saffin, Paul M.
2008-01-01
We investigate the nature of resonant tunneling in standard scalar Quantum Field Theory. Following the pioneering work of Banks, Bender and Wu we describe the quantum field theory in terms of infinite dimensional quantum mechanics and utilize the ``Most probable escape path'' (MPEP) as the class of paths which dominate the path integral in the classically forbidden region. Considering a 1+1 dimensional field theory example we show that there are five conditions that any associated bound state in the classically allowed region must satisfy if resonant tunnelling is to occur, and we then proceed to show that it is impossible to satisfy all five conditions simultaneously.
Gravity Dual for Reggeon Field Theory and Nonlinear Quantum Finance
NASA Astrophysics Data System (ADS)
Nakayama, Yu
We study scale invariant but not necessarily conformal invariant deformations of nonrelativistic conformal field theories from the dual gravity viewpoint. We present the corresponding metric that solves the Einstein equation coupled with a massive vector field. We find that, within the class of metric we study, when we assume the Galilean invariance, the scale invariant deformation always preserves the nonrelativistic conformal invariance. We discuss applications to scaling regime of Reggeon field theory and nonlinear quantum finance. These theories possess scale invariance but may or may not break the conformal invariance, depending on the underlying symmetry assumptions.
Doubled Field Theory, T-Duality and Courant-Brackets
NASA Astrophysics Data System (ADS)
Zwiebach, Barton
In these lecture notes we give a simple introduction into double field theory. We show that the presence of momentum and winding excitations in toroidal backgrounds of closed string theory makes it natural to consider double field theories. A tool-kit is developed based on the Courant-bracket and generalized Lie derivatives. We construct a background independent action which represents a T-duality covariantization of the Einstein-Hilbert action for gravity coupled to an antisymmetric tensor field and a dilaton.
Incorporation of generalized uncertainty principle into Lifshitz field theories
Faizal, Mir; Majumder, Barun
2015-06-15
In this paper, we will incorporate the generalized uncertainty principle into field theories with Lifshitz scaling. We will first construct both bosonic and fermionic theories with Lifshitz scaling based on generalized uncertainty principle. After that we will incorporate the generalized uncertainty principle into a non-abelian gauge theory with Lifshitz scaling. We will observe that even though the action for this theory is non-local, it is invariant under local gauge transformations. We will also perform the stochastic quantization of this Lifshitz fermionic theory based generalized uncertainty principle.
Hitchin equation, singularity, and N = 2 superconformal field theories
NASA Astrophysics Data System (ADS)
Nanopoulos, Dimitri; Xie, Dan
2010-03-01
We argue that Hitchin’s equation determines not only the low energy effective theory but also describes the UV theory of four dimensional N = 2 superconformal field theories when we compactify six dimensional A N (0, 2) theory on a punctured Riemann surface. We study singular solutions to Hitchin’s equation and the Highs field of equation has a simple pole at the punctures; We show that the massless theory is associated with Higgs field whose residue is a nilpotent element; We identify the flavor symmetry associated with the puncture by studying the singularity of closure of the moduli space of solutions with the appropriate boundary conditions. For mass-deformed theory the residue of the Higgs field is a semi-simple element, we identify the semi-simple element by arguing that the moduli space of solutions of mass-deformed theory must be a deformation of the closure of the moduli space of massless theory. We also study the Seiberg-Witten curve by identifying it as the spectral curve of the Hitchin’s system. The results are all in agreement with Gaiotto’s results derived from studying the Seiberg-Witten curve of four dimensional quiver gauge theory.
Prolonged Field Care Working Group Fluid Therapy Recommendations.
Baker, Benjamin L; Powell, Doug; Riesberg, Jamie; Keenan, Sean
2016-01-01
The Prolonged Field Care Working Group concurs that fresh whole blood (FWB) is the fluid of choice for patients in hemorrhagic shock, and the capability to transfuse FWB should be a basic skill set for Special Operations Forces (SOF) Medics. Prolonged field care (PFC) must also address resuscitative and maintenance fluid requirements in nonhemorrhagic conditions. PMID:27045508
The Theory of Quantized Fields. III
DOE R&D Accomplishments Database
Schwinger, J.
1953-05-01
In this paper we discuss the electromagnetic field, as perturbed by a prescribed current. All quantities of physical interest in various situations, eigenvalues, eigenfunctions, and transformation probabilities, are derived from a general transformation function which is expressed in a non-Hermitian representation. The problems treated are: the determination of the energy-momentum eigenvalues and eigenfunctions for the isolated electromagnetic field, and the energy eigenvalues and eigenfunctions for the field perturbed by a time-independent current that departs from zero only within a finite time interval, and for a time-dependent current that assumes non-vanishing time-independent values initially and finally. The results are applied in a discussion of the intra-red catastrophe and of the adiabatic theorem. It is shown how the latter can be exploited to give a uniform formulation for all problems requiring the evaluation of transition probabilities or eigenvalue displacements.
A New Lorentz Violating Nonlocal Field Theory From String-Theory
Ganor, Ori J.
2007-10-04
A four-dimensional field theory with a qualitatively new type of nonlocality is constructed from a setting where Kaluza-Klein particles probe toroidally compactified string theory with twisted boundary conditions. In this theory fundamental particles are not pointlike and occupy a volume proportional to their R-charge. The theory breaks Lorentz invariance but appears to preserve spatial rotations. At low energies, it is approximately N=4 Super Yang-Mills theory, deformed by an operator of dimension seven. The dispersion relation of massless modes in vacuum is unchanged, but under certain conditions in this theory, particles can travel at superluminal velocities.
Lattice Study of Magnetic Catalysis in Graphene Effective Field Theory
NASA Astrophysics Data System (ADS)
Winterowd, Christopher; Detar, Carleton; Zafeiropoulos, Savvas
2016-03-01
The discovery of graphene ranks as one of the most important developments in condensed matter physics in recent years. As a strongly interacting system whose low-energy excitations are described by the Dirac equation, graphene has many similarities with other strongly interacting field theories, particularly quantum chromodynamics (QCD). Graphene, along with other relativistic field theories, have been predicted to exhibit spontaneous symmetry breaking (SSB) when an external magnetic field is present. Using nonperturbative methods developed to study QCD, we study the low-energy effective field theory (EFT) of graphene subject to an external magnetic field. We find strong evidence supporting the existence of SSB at zero-temperature and characterize the dependence of the chiral condensate on the external magnetic field. We also present results for the mass of the Nambu-Goldstone boson and the dynamically generated quasiparticle mass that result from the SSB.
Screening of scalar fields in Dirac-Born-Infeld theory
NASA Astrophysics Data System (ADS)
Burrage, Clare; Khoury, Justin
2014-07-01
We study a new screening mechanism which is present in Dirac-Born-Infeld (DBI)-like theories. A scalar field with a DBI-like Lagrangian is minimally coupled to matter. In the vicinity of sufficiently dense sources, nonlinearities in the scalar dominate and result in an approximately constant acceleration on a test particle, thereby suppressing the scalar force relative to gravity. Unlike generic P(X) or chameleon theories, screening happens within the regime of validity of the effective field theory thanks to the DBI symmetry. We derive an exact form for the field profile around multiple sources and determine the constraints on the theory parameters from tests of gravity. Perturbations around the spherically-symmetric background propagate superluminally, but we argue for a chronology protection analogous to Galileons. This is the first example of a screening mechanism for which quantum corrections to the theory are under control and exact solutions to cosmological N-body problems can be found.
Topological Field Theory of Time-Reversal Invariant Insulators
Qi, Xiao-Liang; Hughes, Taylor; Zhang, Shou-Cheng; /Stanford U., Phys. Dept.
2010-03-19
We show that the fundamental time reversal invariant (TRI) insulator exists in 4 + 1 dimensions, where the effective field theory is described by the 4 + 1 dimensional Chern-Simons theory and the topological properties of the electronic structure is classified by the second Chern number. These topological properties are the natural generalizations of the time reversal breaking (TRB) quantum Hall insulator in 2 + 1 dimensions. The TRI quantum spin Hall insulator in 2 + 1 dimensions and the topological insulator in 3 + 1 dimension can be obtained as descendants from the fundamental TRI insulator in 4 + 1 dimensions through a dimensional reduction procedure. The effective topological field theory, and the Z{sub 2} topological classification for the TRI insulators in 2+1 and 3+1 dimensions are naturally obtained from this procedure. All physically measurable topological response functions of the TRI insulators are completely described by the effective topological field theory. Our effective topological field theory predicts a number of novel and measurable phenomena, the most striking of which is the topological magneto-electric effect, where an electric field generates a magnetic field in the same direction, with an universal constant of proportionality quantized in odd multiples of the fine structure constant {alpha} = e{sup 2}/hc. Finally, we present a general classification of all topological insulators in various dimensions, and describe them in terms of a unified topological Chern-Simons field theory in phase space.
Conceptual Developments of 20th Century Field Theories
NASA Astrophysics Data System (ADS)
Cao, Tian Yu
1998-06-01
This volume provides a broad synthesis of conceptual developments of twentieth century field theories, from the general theory of relativity to quantum field theory and gauge theory. The book traces the foundations and evolution of these theories within a historio-critical context. Theoretical physicists and students of theoretical physics will find this a valuable account of the foundational problems of their discipline that will help them understand the internal logic and dynamics of theoretical physics. It will also provide professional historians and philosophers of science, particularly philosophers of physics, with a conceptual basis for further historical, cultural and sociological analysis of the theories discussed. Finally, the scientifically qualified general reader will find in this book a deeper analysis of contemporary conceptions of the physical world than can be found in popular accounts of the subject.
Conceptual Developments of 20th Century Field Theories
NASA Astrophysics Data System (ADS)
Cao, Tian Yu
1997-02-01
This volume provides a broad synthesis of conceptual developments of twentieth century field theories, from the general theory of relativity to quantum field theory and gauge theory. The book traces the foundations and evolution of these theories within a historio-critical context. Theoretical physicists and students of theoretical physics will find this a valuable account of the foundational problems of their discipline that will help them understand the internal logic and dynamics of theoretical physics. It will also provide professional historians and philosophers of science, particularly philosophers of physics, with a conceptual basis for further historical, cultural and sociological analysis of the theories discussed. Finally, the scientifically qualified general reader will find in this book a deeper analysis of contemporary conceptions of the physical world than can be found in popular accounts of the subject.
Theory of back-surface-field solar cells
NASA Technical Reports Server (NTRS)
Vonroos, O.
1979-01-01
Report describes simple concise theory of back-surface-field (BSF) solar cells (npp + junctions) based on Shockley's depletion-layer approximation and cites superiority of two-junction devices over conventional unijunction cells.
Background field functional renormalization group for absorbing state phase transitions.
Buchhold, Michael; Diehl, Sebastian
2016-07-01
We present a functional renormalization group approach for the active to inactive phase transition in directed percolation-type systems, in which the transition is approached from the active, finite density phase. By expanding the effective potential for the density field around its minimum, we obtain a background field action functional, which serves as a starting point for the functional renormalization group approach. Due to the presence of the background field, the corresponding nonperturbative flow equations yield remarkably good estimates for the critical exponents of the directed percolation universality class, even in low dimensions. PMID:27575107
Background field functional renormalization group for absorbing state phase transitions
NASA Astrophysics Data System (ADS)
Buchhold, Michael; Diehl, Sebastian
2016-07-01
We present a functional renormalization group approach for the active to inactive phase transition in directed percolation-type systems, in which the transition is approached from the active, finite density phase. By expanding the effective potential for the density field around its minimum, we obtain a background field action functional, which serves as a starting point for the functional renormalization group approach. Due to the presence of the background field, the corresponding nonperturbative flow equations yield remarkably good estimates for the critical exponents of the directed percolation universality class, even in low dimensions.
Perturbation Theory of Massive Yang-Mills Fields
DOE R&D Accomplishments Database
Veltman, M.
1968-08-01
Perturbation theory of massive Yang-Mills fields is investigated with the help of the Bell-Treiman transformation. Diagrams containing one closed loop are shown to be convergent if there are more than four external vector boson lines. The investigation presented does not exclude the possibility that the theory is renormalizable.
A Guided Inquiry Activity for Teaching Ligand Field Theory
ERIC Educational Resources Information Center
Johnson, Brian J.; Graham, Kate J.
2015-01-01
This paper will describe a guided inquiry activity for teaching ligand field theory. Previous research suggests the guided inquiry approach is highly effective for student learning. This activity familiarizes students with the key concepts of molecular orbital theory applied to coordination complexes. Students will learn to identify factors that…
Constrained variational calculus for higher order classical field theories
NASA Astrophysics Data System (ADS)
Campos, Cédric M.; de León, Manuel; Martín de Diego, David
2010-11-01
We develop an intrinsic geometrical setting for higher order constrained field theories. As a main tool we use an appropriate generalization of the classical Skinner-Rusk formalism. Some examples of applications are studied, in particular to the geometrical description of optimal control theory for partial differential equations.
Scalar field theory in {kappa}-Minkowski spacetime from twist
Kim, Hyeong-Chan; Lee, Youngone; Rim, Chaiho; Yee, Jae Hyung
2009-10-15
Using the twist deformation of U(igl(4,R)), the linear part of the diffeomorphism, we define a scalar function and construct a free scalar field theory in four-dimensional {kappa}-Minkowski spacetime. The action in momentum space turns out to differ only in the integration measure from the commutative theory.
Near-field environment/processes working group summary
Murphy, W.M.
1995-09-01
This article is a summary of the proceedings of a group discussion which took place at the Workshop on the Role of Natural Analogs in Geologic Disposal of High-Level Nuclear Waste in San Antonio, Texas on July 22-25, 1991. The working group concentrated on the subject of the near-field environment to geologic repositories for high-level nuclear waste. The near-field environment may be affected by thermal perturbations from the waste, and by disturbances caused by the introduction of exotic materials during construction of the repository. This group also discussed the application of modelling of performance-related processes.
The Lagrangian-Hamiltonian formalism for higher order field theories
NASA Astrophysics Data System (ADS)
Vitagliano, Luca
2010-06-01
We generalize the Lagrangian-Hamiltonian formalism of Skinner and Rusk to higher order field theories on fiber bundles. As a byproduct we solve the long standing problem of defining, in a coordinate free manner, a Hamiltonian formalism for higher order Lagrangian field theories. Namely, our formalism does only depend on the action functional and, therefore, unlike previously proposed ones, is free from any relevant ambiguity.
Quantum Field Theory in Coordinate Space
NASA Astrophysics Data System (ADS)
Erdogan, Ahmet Ozan
In order to provide a new coordinate-space perspective applicable to scattering amplitudes, in the first part of this dissertation, the structure of singularities in perturbative massless gauge theories is investigated in coordinate space. The pinch singularities in coordinate-space integrals occur at configurations of vertices which have a direct interpretation in terms of physical scattering of particles in real space-time in the same way as for the loop momenta in the case of momentum-space singularities. In the analysis of vertex functions in coordinate space, the well-known factorization into hard, soft, and jet functions is found. By power-counting arguments, it is found that coordinate-space integrals of vertex functions have logarithmic divergences at worst. The `hard-collinear' and `soft-collinear' approximations that allow the application of gauge theory Ward identities in the formal proof of factorization in coordinate space are introduced. In the second part, the perturbative cusp and closed polygons of Wilson lines for massless gauge theories are analyzed in coordinate space, and expressed as exponentials of two-dimensional integrals. These integrals have geometric interpretations, which link renormalization scales with invariant distances. A direct perturbative prescription for the logarithm of the cusp and related cross sections treated in eikonal approximation is provided by web diagrams. The sources of their ultraviolet poles in coordinate space associated with their nonlocal collinear divergences are identified by the power-counting technique explained in the first part. In the study of the coordinate-space matrix elements that correspond to scattering amplitudes involving partons and Wilson lines in coordinate space, a series of subtractions is developed to eliminate their divergences and to show their factorization in coordinate space. The ultraviolet finiteness of the web integrand is shown by relating the web expansion to the application of
The mass-zero spin-two field and gravitational theory.
NASA Technical Reports Server (NTRS)
Coulter, C. A.
1972-01-01
Demonstration that the conventional theory of the mass-zero spin-two field with sources introduces extraneous nonspin-two field components in source regions and fails to be covariant under the full or restricted conformal group. A modified theory is given, expressed in terms of the physical components of mass-zero spin-two field rather than in terms of 'potentials,' which has no extraneous components inside or outside sources, and which is covariant under the full conformal group. For a proper choice of source term, this modified theory has the correct Newtonian limit and automatically implies that a symmetric second-rank source tensor has zero divergence. It is shown that possibly a generally covariant form of the spin-two theory derived here can be constructed to agree with general relativity in all currently accessible experimental situations.
Effective hydrodynamic field theory and condensation picture of topological insulators
NASA Astrophysics Data System (ADS)
Chan, AtMa P. O.; Kvorning, Thomas; Ryu, Shinsei; Fradkin, Eduardo
2016-04-01
While many features of topological band insulators are commonly discussed at the level of single-particle electron wave functions, such as the gapless Dirac boundary spectrum, it remains elusive to develop a hydrodynamic or collective description of fermionic topological band insulators in 3+1 dimensions. As the Chern-Simons theory for the 2+1-dimensional quantum Hall effect, such a hydrodynamic effective field theory provides a universal description of topological band insulators, even in the presence of interactions, and that of putative fractional topological insulators. In this paper, we undertake this task by using the functional bosonization. The effective field theory in the functional bosonization is written in terms of a two-form gauge field, which couples to a U (1 ) gauge field that arises by gauging the continuous symmetry of the target system [the U (1 ) particle number conservation]. Integrating over the U (1 ) gauge field by using the electromagnetic duality, the resulting theory describes topological band insulators as a condensation phase of the U (1 ) gauge theory (or as a monopole condensation phase of the dual gauge field). The hydrodynamic description of the surface of topological insulators and the implication of its duality are also discussed. We also touch upon the hydrodynamic theory of fractional topological insulators by using the parton construction.
NASA Astrophysics Data System (ADS)
Méliot, Pierre-Loïc
2010-12-01
In this thesis, we investigate the asymptotics of random partitions chosen according to probability measures coming from the representation theory of the symmetric groups S_n and of the finite Chevalley groups GL(n,F_q) and Sp(2n,F_q). More precisely, we prove laws of large numbers and central limit theorems for the q-Plancherel measures of type A and B, the Schur-Weyl measures and the Gelfand measures. Using the RSK algorithm, it also gives results on longest increasing subsequences in random words. We develop a technique of moments (and cumulants) for random partitions, thereby using the polynomial functions on Young diagrams in the sense of Kerov and Olshanski. The algebra of polynomial functions, or observables of Young diagrams is isomorphic to the algebra of partial permutations; in the last part of the thesis, we try to generalize this beautiful construction.
NASA Astrophysics Data System (ADS)
Popov, V. S.
2007-12-01
Feynman's method for disentangling noncommuting operators is discussed and applied to nonstationary problems in quantum mechanics, including the excitation of a harmonic oscillator by an external force and/or by time-varying frequency; spin rotation in a time-varying magnetic field; the disentangling of an atom (ion) Hamiltonian in a laser field; a model with the hidden symmetry group of the hydrogen atom; and the theory of coherent states. The Feynman operator calculus combined with simple group-theoretical considerations allows disentangling the Hamiltonian and obtaining exact transition probabilities between the initial and final states of a quantum oscillator in analytic form without cumbersome calculations. The case of a D-dimensional oscillator is briefly discussed, in particular, in application to the problem of vacuum pair creation in an intense electric field.
On the renormalization of non-commutative field theories
NASA Astrophysics Data System (ADS)
Blaschke, Daniel N.; Garschall, Thomas; Gieres, François; Heindl, Franz; Schweda, Manfred; Wohlgenannt, Michael
2013-01-01
This paper addresses three topics concerning the quantization of non-commutative field theories (as defined in terms of the Moyal star product involving a constant tensor describing the non-commutativity of coordinates in Euclidean space). To start with, we discuss the Quantum Action Principle and provide evidence for its validity for non-commutative quantum field theories by showing that the equation of motion considered as insertion in the generating functional Z c [ j] of connected Green functions makes sense (at least at one-loop level). Second, we consider the generalization of the BPHZ renormalization scheme to non-commutative field theories and apply it to the case of a self-interacting real scalar field: Explicit computations are performed at one-loop order and the generalization to higher loops is commented upon. Finally, we discuss the renormalizability of various models for a self-interacting complex scalar field by using the approach of algebraic renormalization.
Conformal field theories with infinitely many conservation laws
Todorov, Ivan
2013-02-15
Globally conformal invariant quantum field theories in a D-dimensional space-time (D even) have rational correlation functions and admit an infinite number of conserved (symmetric traceless) tensor currents. In a theory of a scalar field of dimension D-2 they were demonstrated to be generated by bilocal normal products of free massless scalar fields with an O(N), U(N), or Sp(2N) (global) gauge symmetry [B. Bakalov, N. M. Nikolov, K.-H. Rehren, and I. Todorov, 'Unitary positive energy representations of scalar bilocal fields,' Commun. Math. Phys. 271, 223-246 (2007); e-print arXiv:math-ph/0604069v3; and 'Infinite dimensional Lie algebras in 4D conformal quantum field theory,' J. Phys. A Math Theor. 41, 194002 (2008); e-print arXiv:0711.0627v2 [hep-th
Statistical field theory description of inhomogeneous polarizable soft matter
NASA Astrophysics Data System (ADS)
Martin, Jonathan M.; Li, Wei; Delaney, Kris T.; Fredrickson, Glenn H.
2016-10-01
We present a new molecularly informed statistical field theory model of inhomogeneous polarizable soft matter. The model is based on fluid elements, referred to as beads, that can carry a net monopole of charge at their center of mass and a fixed or induced dipole through a Drude-type distributed charge approach. The beads are thus polarizable and naturally manifest attractive van der Waals interactions. Beyond electrostatic interactions, beads can be given soft repulsions to sustain fluid phases at arbitrary densities. Beads of different types can be mixed or linked into polymers with arbitrary chain models and sequences of charged and uncharged beads. By such an approach, it is possible to construct models suitable for describing a vast range of soft-matter systems including electrolyte and polyelectrolyte solutions, ionic liquids, polymerized ionic liquids, polymer blends, ionomers, and block copolymers, among others. These bead models can be constructed in virtually any ensemble and converted to complex-valued statistical field theories by Hubbard-Stratonovich transforms. One of the fields entering the resulting theories is a fluctuating electrostatic potential; other fields are necessary to decouple non-electrostatic interactions. We elucidate the structure of these field theories, their consistency with macroscopic electrostatic theory in the absence and presence of external electric fields, and the way in which they embed van der Waals interactions and non-uniform dielectric properties. Their suitability as a framework for computational studies of heterogeneous soft matter systems using field-theoretic simulation techniques is discussed.
Democracy of internal symmetries in supersymmetrical quantum field theory
Lopuszanski, J.T.
1981-12-01
The freedom of choice of some discrete and internal symmetries in the supersymmetric, massive, interacting quantum field theory is discussed. It is shown that the discrete symmetry consisting of changing the sign of some (not all) scalar fields is incompatible with the supersymmetric structure of the theory. It is further demonstrated that an internal symmetry which transforms only some of the fields of fixed spin leaving the other fields invariant and which acts nontrivially on the supercharges can not be admitted as a symmetry; although it can be a good internal symmetry in absence of supersymmetric covariance. Moreover, in case of a model consisting of scalar, spinor and vector fields even a symmetry which transforms all of the scalar (vector) fields leaving spinor and vector (scalar) fields unaffected is ruled out provided it acts nontrivially on some of the supercharges.
Low energy signatures of nonlocal field theories
NASA Astrophysics Data System (ADS)
Belenchia, Alessio; Benincasa, Dionigi M. T.; Martín-Martínez, Eduardo; Saravani, Mehdi
2016-09-01
The response of inertial particle detectors coupled to a scalar field satisfying nonlocal dynamics described by nonanalytic functions of the d'Alembertian operator □ is studied. We show that spontaneous emission processes of a low energy particle detector are very sensitive to high-energy nonlocality scales. This allows us to suggest a nuclear physics experiment (˜MeV energy scales) that outperforms the sensitivity of LHC experiments by many orders of magnitude. This may have implications for the falsifiability of theoretical proposals of quantum gravity.
Very special relativity as a background field theory
NASA Astrophysics Data System (ADS)
Ilderton, Anton
2016-08-01
We consider violation of Lorentz invariance in QED induced by a very high frequency background wave. An effective theory is obtained by averaging observables over the rapid field oscillations. This preserves Ward identities and restores translation invariance below the high-frequency scale, but only partial Lorentz invariance: we show that the effective theory is C-invariant SIM(2)-QED in very special relativity. Averaging leads to the nonlocal terms familiar from SIM(2) theories, while the short-distance behavior of the background field fermion propagator generates the infinite number of higher-order vertices of SIM(2)-QED.
Generating functionals for quantum field theories with random potentials
NASA Astrophysics Data System (ADS)
Jain, Mudit; Vanchurin, Vitaly
2016-01-01
We consider generating functionals for computing correlators in quantum field theories with random potentials. Examples of such theories include cosmological systems in context of the string theory landscape (e.g. cosmic inflation) or condensed matter systems with quenched disorder (e.g. spin glass). We use the so-called replica trick to define two different generating functionals for calculating correlators of the quantum fields averaged over a given distribution of random potentials. The first generating functional is appropriate for calculating averaged (in-out) amplitudes and involves a single replica of fields, but the replica limit is taken to an (unphysical) negative one number of fields outside of the path integral. When the number of replicas is doubled the generating functional can also be used for calculating averaged probabilities (squared amplitudes) using the in-in construction. The second generating functional involves an infinite number of replicas, but can be used for calculating both in-out and in-in correlators and the replica limits are taken to only a zero number of fields. We discuss the formalism in details for a single real scalar field, but the generalization to more fields or to different types of fields is straightforward. We work out three examples: one where the mass of scalar field is treated as a random variable and two where the functional form of interactions is random, one described by a Gaussian random field and the other by a Euclidean action in the field configuration space.
DBI scalar field theory for QGP hydrodynamics
NASA Astrophysics Data System (ADS)
Nastase, Horatiu
2016-07-01
A way to describe the hydrodynamics of the quark-gluon plasma using a Dirac-Born-Infeld (DBI) action is proposed, based on the model found by Heisenberg for high energy scattering of nucleons. The expanding plasma is described as a shockwave in a DBI model for a real scalar standing in for the pion, and I show that one obtains a fluid description in terms of a relativistic fluid that near the shock is approximately ideal (η ≃0 ) and conformal. One can introduce an extra term inside the square root of the DBI action that generates a shear viscosity term in the energy-momentum tensor near the shock, as well as a bulk viscosity, and regulates the behavior of the energy density at the shock, making it finite. The resulting fluid satisfies the relativistic Navier-Stokes equation with uμ,ρ ,P ,η defined in terms of ϕ and its derivatives. One finds a relation between the parameters of the theory and the quark-gluon plasma thermodynamics, α /β2=η /(s T ), and by fixing α and β from usual (low multiplicity) particle scattering, one finds T ∝mπ.
Continuum regularization of quantum field theory
Bern, Z.
1986-01-01
Breit, Gupta, and Zaks made the first proposal for new gauge invariant nonperturbative regularization. The scheme is based on smearing in the fifth-time of the Langevin equation. An analysis of their stochastic regularization scheme for the case of scalar electrodynamics with the standard covariant gauge fixing is given. Their scheme is shown to preserve the masslessness of the photon and the tensor structure of the photon vacuum polarization at the one-loop level. Although stochastic regularization is viable in one-loop electrodynamics, difficulties arise which, in general, ruins the scheme. A successful covariant derivative scheme is discussed which avoids the difficulties encountered with the earlier stochastic regularization by fifth-time smearing. For QCD the regularized formulation is manifestly Lorentz invariant, gauge invariant, ghost free and finite to all orders. A vanishing gluon mass is explicitly verified at one loop. The method is designed to respect relevant symmetries, and is expected to provide suitable regularization for any theory of interest.
Graphene, Lattice Field Theory and Symmetries
Drissi, L. B.; Bousmina, M.; Saidi, E. H.
2011-02-15
Borrowing ideas from tight binding model, we propose a board class of lattice field models that are classified by non simply laced Lie algebras. In the case of A{sub N-1{approx_equal}}su(N) series, we show that the couplings between the quantum states living at the first nearest neighbor sites of the lattice L{sub suN} are governed by the complex fundamental representations N-bar and N of su(N) and the second nearest neighbor interactions are described by its adjoint N-bar x N. The lattice models associated with the leading su(2), su(3), and su(4) cases are explicitly studied and their fermionic field realizations are given. It is also shown that the su(2) and su(3) models describe the electronic properties of the acetylene chain and the graphene, respectively. It is established as well that the energy dispersion of the first nearest neighbor couplings is completely determined by the A{sub N} roots {alpha} through the typical dependence N/2+{Sigma}{sub roots} cos(k.{alpha} with k the wave vector.Other features such as the SO(2N) extension and other applications are also discussed.
Field Theoretic Formulation of Kinetic Theory: Basic Development
NASA Astrophysics Data System (ADS)
Das, Shankar P.; Mazenko, Gene F.
2012-11-01
We show how kinetic theory, the statistics of classical particles obeying Newtonian dynamics, can be formulated as a field theory. The field theory can be organized to produce a self-consistent perturbation theory expansion in an effective interaction potential. The need for a self-consistent approach is suggested by our interest in investigating ergodic-nonergodic transitions in dense fluids. The formal structure we develop has been implemented in detail for the simpler case of Smoluchowski dynamics. One aspect of the approach is the identification of a core problem spanned by the variables ρ the number density and B a response density. In this paper we set up the perturbation theory expansion with explicit development at zeroth and first order. We also determine all of the cumulants in the noninteracting limit among the core variables ρ and B.
Ordinary versus PT-symmetric Φ³ quantum field theory
Bender, Carl M.; Branchina, Vincenzo; Messina, Emanuele
2012-04-02
A quantum-mechanical theory is PT-symmetric if it is described by a Hamiltonian that commutes with PT, where the operator P performs space reflection and the operator T performs time reversal. A PT-symmetric Hamiltonian often has a parametric region of unbroken PT symmetry in which the energy eigenvalues are all real. There may also be a region of broken PT symmetry in which some of the eigenvalues are complex. These regions are separated by a phase transition that has been repeatedly observed in laboratory experiments. This paper focuses on the properties of a PT-symmetric igΦ³ quantum field theory. This quantum field theory is the analog of the PT-symmetric quantum-mechanical theory described by the Hamiltonian H=p²+ix³, whose eigenvalues have been rigorously shown to be all real. This paper compares the renormalization group properties of a conventional Hermitian gΦ³ quantum field theory with those of the PT-symmetric igΦ³ quantum field theory. It is shown that while the conventional gΦ³ theory in d=6 dimensions is asymptotically free, the igΦ³ theory is like a gΦ⁴ theory in d=4 dimensions; it is energetically stable, perturbatively renormalizable, and trivial.
Some equivalences between the auxiliary field method and envelope theory
Buisseret, Fabien; Semay, Claude; Silvestre-Brac, Bernard
2009-03-15
The auxiliary field method has been recently proposed as an efficient technique to compute analytical approximate solutions of eigenequations in quantum mechanics. We show that the auxiliary field method is completely equivalent to the envelope theory, which is another well-known procedure to analytically solve eigenequations, although relying on different principles a priori. This equivalence leads to a deeper understanding of both frameworks.
Dualities among one-time field theories with spin, emerging from a unifying two-time field theory
Bars, Itzhak; Quelin, Guillaume
2008-06-15
The relation between two-time physics (2T-physics) and the ordinary one-time formulation of physics (1T-physics) is similar to the relation between a 3-dimensional object moving in a room and its multiple shadows moving on walls when projected from different perspectives. The multiple shadows as seen by observers stuck on the wall are analogous to the effects of the 2T-universe as experienced in ordinary 1T spacetime. In this paper we develop some of the quantitative aspects of this 2T to 1T relationship in the context of field theory. We discuss 2T field theory in d+2 dimensions and its shadows in the form of 1T field theories when the theory contains Klein-Gordon, Dirac and Yang-Mills fields, such as the standard model of particles and forces. We show that the shadow 1T field theories must have hidden relations among themselves. These relations take the form of dualities and hidden spacetime symmetries. A subset of the shadows are 1T field theories in different gravitational backgrounds (different space-times) such as the flat Minkowski spacetime, the Robertson-Walker expanding universe, AdS{sub d-k}xS{sup k}, and others, including singular ones. We explicitly construct the duality transformations among this conformally flat subset, and build the generators of their hidden SO(d,2) symmetry. The existence of such hidden relations among 1T field theories, which can be tested by both theory and experiment in 1T-physics, is part of the evidence for the underlying d+2 dimensional spacetime and the unifying 2T-physics structure.
Improved renormalization group theory for critical asymmetry of fluids
NASA Astrophysics Data System (ADS)
Wang, Long; Zhao, Wei; Wu, Liang; Li, Liyan; Cai, Jun
2013-09-01
We develop an improved renormalization group (RG) approach incorporating the critical vapor-liquid equilibrium asymmetry. In order to treat the critical asymmetry of vapor-liquid equilibrium, the integral measure is introduced in the Landau-Ginzbug partition function to achieve a crossover between the local order parameter in Ising model and the density of fluid systems. In the implementation of the improved RG approach, we relate the integral measure with the inhomogeneous density distribution of a fluid system and combine the developed method with SAFT-VR (statistical associating fluid theory of variable range) equation of state. The method is applied to various fluid systems including square-well fluid, square-well dimer fluid and real fluids such as methane (CH4), ethane (C2H6), trifluorotrichloroethane (C2F3Cl3), and sulfur hexafluoride (SF6). The descriptions of vapor-liquid equilibria provided by the developed method are in excellent agreement with simulation and experimental data. Furthermore, the improved method predicts accurate and qualitatively correct behavior of coexistence diameter near the critical point and produces the non-classical 3D Ising criticality.
Quantum field theory constrains traversable wormhole geometries
Ford, L.H. |; Roman, T.A. |
1996-05-01
Recently a bound on negative energy densities in four-dimensional Minkowski spacetime was derived for a minimally coupled, quantized, massless, scalar field in an arbitrary quantum state. The bound has the form of an uncertainty-principle-type constraint on the magnitude and duration of the negative energy density seen by a timelike geodesic observer. When spacetime is curved and/or has boundaries, we argue that the bound should hold in regions small compared to the minimum local characteristic radius of curvature or the distance to any boundaries, since spacetime can be considered approximately Minkowski on these scales. We apply the bound to the stress-energy of static traversable wormhole spacetimes. Our analysis implies that either the wormhole must be only a little larger than Planck size or that there is a large discrepancy in the length scales which characterize the wormhole. In the latter case, the negative energy must typically be concentrated in a thin band many orders of magnitude smaller than the throat size. These results would seem to make the existence of macroscopic traversable wormholes very improbable. {copyright} {ital 1996 The American Physical Society.}
A gauge field theory of fermionic continuous-spin particles
NASA Astrophysics Data System (ADS)
Bekaert, X.; Najafizadeh, M.; Setare, M. R.
2016-09-01
In this letter, we suggest a local covariant action for a gauge field theory of fermionic Continuous-Spin Particles (CSPs). The action is invariant under gauge transformations without any constraint on both the gauge field and the gauge transformation parameter. The Fang-Fronsdal equations for a tower of massless fields with all half-integer spins arise as a particular limit of the equation of motion of fermionic CSPs.
Massive basketball diagram for a thermal scalar field theory
NASA Astrophysics Data System (ADS)
Andersen, Jens O.; Braaten, Eric; Strickland, Michael
2000-08-01
The ``basketball diagram'' is a three-loop vacuum diagram for a scalar field theory that cannot be expressed in terms of one-loop diagrams. We calculate this diagram for a massive scalar field at nonzero temperature, reducing it to expressions involving three-dimensional integrals that can be easily evaluated numerically. We use this result to calculate the free energy for a massive scalar field with a φ4 interaction to three-loop order.
Quantum Field Theory in Curved Spacetime
NASA Astrophysics Data System (ADS)
Reynolds, Sally C.; Gallagher, Andrew
2012-03-01
List of contributors; Foreword J. T. Francis Thackeray; 1. African genesis: an evolving paradigm Sally C. Reynolds; 2. Academic genealogy Peter Ungar and Phillip V. Tobias; Part I. In Search of Origins: Evolutionary Theory, New Species, and Paths into the Past: 3. Speciation in hominin evolution Colin Groves; 4. Searching for a new paradigm for hominid origins in Chad (Central Africa) Michel Brunet; 5. From hominoid arboreality to hominid bipedalism Brigitte Senut; 6. Orrorin and the African ape/hominid dichotomy Martin Pickford; 7. A brief history and results of 40 years of Sterkfontein excavations Ronald J. Clarke; Part II. Hominin Morphology Through Time: Brains, Bodies and Teeth: 8. Hominin brain evolution, 1925-2011: an emerging overview Dean Falk; 9. The issue of brain reorganisation in Australopithecus and early hominids: Dart had it right Ralph L. Holloway; 10. The mass of the human brain: is it a spandrel? Paul R. Manger, Jason Hemingway, Muhammad Spocter and Andrew Gallagher; 11. Origin and diversity of early hominin bipedalism Henry M. McHenry; 12. Forelimb adaptations in Australopithecus afarensis Michelle S. M. Drapeau; 13. Hominin proximal femur morphology from the Tugen Hills to Flores Brian G. Richmond and William L. Jungers; 14. Daily rates of dentine formation and root extension rates in Paranthropus boisei, KNM-ER 1817, from Koobi Fora, Kenya M. Christopher Dean; 15. On the evolutionary development of early hominid molar teeth and the Gondolin Paranthropus molar Kevin L. Kuykendall; 16. Digital South African fossils: morphological studies using reference-based reconstruction and electronic preparation Gerhard W. Weber, Philipp Gunz, Simon Neubauer, Philipp Mitteroecker and Fred L. Bookstein; Part III. Modern Human Origins: Patterns, and Processes: 17. Body size in African Middle Pleistocene Homo Steven E. Churchill, Lee R. Berger, Adam Hartstone-Rose and Headman Zondo; 18. The African origin of recent humanity Milford H. Wolpoff and Sang-Hee Lee
Carlson, Rebecca K; Li Manni, Giovanni; Sonnenberger, Andrew L; Truhlar, Donald G; Gagliardi, Laura
2015-01-13
Kohn-Sham density functional theory, resting on the representation of the electronic density and kinetic energy by a single Slater determinant, has revolutionized chemistry, but for open-shell systems, the Kohn-Sham Slater determinant has the wrong symmetry properties as compared to an accurate wave function. We have recently proposed a theory, called multiconfiguration pair-density functional theory (MC-PDFT), in which the electronic kinetic energy and classical Coulomb energy are calculated from a multiconfiguration wave function with the correct symmetry properties, and the rest of the energy is calculated from a density functional, called the on-top density functional, that depends on the density and the on-top pair density calculated from this wave function. We also proposed a simple way to approximate the on-top density functional by translation of Kohn-Sham exchange-correlation functionals. The method is much less expensive than other post-SCF methods for calculating the dynamical correlation energy starting with a multiconfiguration self-consistent-field wave function as the reference wave function, and initial tests of the theory were quite encouraging. Here, we provide a broader test of the theory by applying it to bond energies of main-group molecules and transition metal complexes, barrier heights and reaction energies for diverse chemical reactions, proton affinities, and the water dimerization energy. Averaged over 56 data points, the mean unsigned error is 3.2 kcal/mol for MC-PDFT, as compared to 6.9 kcal/mol for Kohn-Sham theory with a comparable density functional. MC-PDFT is more accurate on average than complete active space second-order perturbation theory (CASPT2) for main-group small-molecule bond energies, alkyl bond dissociation energies, transition-metal-ligand bond energies, proton affinities, and the water dimerization energy.
Janiszewski, Stefan; Karch, Andreas
2013-02-22
We argue that generic nonrelativistic quantum field theories with a holographic description are dual to Hořava gravity. We construct explicit examples of this duality embedded in string theory by starting with relativistic dual pairs and taking a nonrelativistic scaling limit.
More is the Same; Phase Transitions and Mean Field Theories
NASA Astrophysics Data System (ADS)
Kadanoff, Leo P.
2009-12-01
This paper is the first in a series that will look at the theory of phase transitions from the perspectives of physics and the philosophy of science. The series will consider a group of related concepts derived from condensed matter and statistical physics. The key technical ideas go under the names of "singularity", "order parameter", "mean field theory", "variational method", "correlation length", "universality class", "scale changes", and "renormalization". The first four of these will be considered here. In a less technical vein, the question here is how can matter, ordinary matter, support a diversity of forms. We see this diversity each time we observe ice in contact with liquid water or see water vapor (steam) come up from a pot of heated water. Different phases can be qualitatively different in that walking on ice is well within human capacity, but walking on liquid water is proverbially forbidden to ordinary humans. These differences have been apparent to humankind for millennia, but only brought within the domain of scientific understanding since the 1880s. A phase transition is a change from one behavior to another. A first order phase transition involves a discontinuous jump in some statistical variable. The discontinuous property is called the order parameter. Each phase transition has its own order parameter. The possible order parameters range over a tremendous variety of physical properties. These properties include the density of a liquid-gas transition, the magnetization in a ferromagnet, the size of a connected cluster in a percolation transition, and a condensate wave function in a superfluid or superconductor. A continuous transition occurs when the discontinuity in the jump approaches zero. This article is about statistical mechanics and the development of mean field theory as a basis for a partial understanding of phase transition phenomena. Much of the material in this review was first prepared for the Royal Netherlands Academy of Arts and
Super-Group Field Cosmology in Batalin-Vilkovisky Formulation
NASA Astrophysics Data System (ADS)
Upadhyay, Sudhaker
2016-09-01
In this paper we study the third quantized super-group field cosmology, a model in multiverse scenario, in Batalin-Vilkovisky (BV) formulation. Further, we propose the superfield/super-antifield dependent BRST symmetry transformations. Within this formulation we establish connection between the two different solutions of the quantum master equation within the BV formulation.
Effective field theories for QCD with rooted staggered fermions
Bernard, Claude; Golterman, Maarten; Shamir, Yigal
2008-04-01
Even highly improved variants of lattice QCD with staggered fermions show significant violations of taste symmetry at currently accessible lattice spacings. In addition, the 'rooting trick' is used in order to simulate with the correct number of light sea quarks, and this makes the lattice theory nonlocal, even though there is good reason to believe that the continuum limit is in the correct universality class. In order to understand scaling violations, it is thus necessary to extend the construction of the Symanzik effective theory to include rooted staggered fermions. We show how this can be done, starting from a generalization of the renormalization-group approach to rooted staggered fermions recently developed by one of us. We then explain how the chiral effective theory follows from the Symanzik action, and show that it leads to 'rooted' staggered chiral perturbation theory as the correct chiral theory for QCD with rooted staggered fermions. We thus establish a direct link between the renormalization-group based arguments for the correctness of the continuum limit and the success of rooted staggered chiral perturbation theory in fitting numerical results obtained with the rooting trick. In order to develop our argument, we need to assume the existence of a standard partially-quenched chiral effective theory for any local partially-quenched theory. Other technical, but standard, assumptions are also required.
Ordinary versus PT-symmetric Φ³ quantum field theory
Bender, Carl M.; Branchina, Vincenzo; Messina, Emanuele
2012-04-02
A quantum-mechanical theory is PT-symmetric if it is described by a Hamiltonian that commutes with PT, where the operator P performs space reflection and the operator T performs time reversal. A PT-symmetric Hamiltonian often has a parametric region of unbroken PT symmetry in which the energy eigenvalues are all real. There may also be a region of broken PT symmetry in which some of the eigenvalues are complex. These regions are separated by a phase transition that has been repeatedly observed in laboratory experiments. This paper focuses on the properties of a PT-symmetric igΦ³ quantum field theory. This quantum fieldmore » theory is the analog of the PT-symmetric quantum-mechanical theory described by the Hamiltonian H=p²+ix³, whose eigenvalues have been rigorously shown to be all real. This paper compares the renormalization group properties of a conventional Hermitian gΦ³ quantum field theory with those of the PT-symmetric igΦ³ quantum field theory. It is shown that while the conventional gΦ³ theory in d=6 dimensions is asymptotically free, the igΦ³ theory is like a gΦ⁴ theory in d=4 dimensions; it is energetically stable, perturbatively renormalizable, and trivial.« less
Consistent constraints on the Standard Model Effective Field Theory
NASA Astrophysics Data System (ADS)
Berthier, Laure; Trott, Michael
2016-02-01
We develop the global constraint picture in the (linear) effective field theory generalisation of the Standard Model, incorporating data from detectors that operated at PEP, PETRA, TRISTAN, SpS, Tevatron, SLAC, LEPI and LEP II, as well as low energy precision data. We fit one hundred and three observables. We develop a theory error metric for this effective field theory, which is required when constraints on parameters at leading order in the power counting are to be pushed to the percent level, or beyond, unless the cut off scale is assumed to be large, Λ ≳ 3 TeV. We more consistently incorporate theoretical errors in this work, avoiding this assumption, and as a direct consequence bounds on some leading parameters are relaxed. We show how an S, T analysis is modified by the theory errors we include as an illustrative example.
Quantum field theory in spaces with closed timelike curves
NASA Astrophysics Data System (ADS)
Boulware, David G.
1992-11-01
Gott spacetime has closed timelike curves, but no locally anomalous stress energy. A complete orthonormal set of eigenfunctions of the wave operator is found in the special case of a spacetime in which the total deficit angle is 2π. A scalar quantum field theory is constructed using these eigenfunctions. The resultant interacting quantum field theory is not unitary because the field operators can create real, on-shell, particles in the noncausal region. These particles propagate for finite proper time accumulating an arbitrary phase before being annihilated at the same spacetime point as that at which they were created. As a result, the effective potential within the noncausal region is complex, and probability is not conserved. The stress tensor of the scalar field is evaluated in the neighborhood of the Cauchy horizon; in the case of a sufficiently small Compton wavelength of the field, the stress tensor is regular and cannot prevent the formation of the Cauchy horizon.
Large field inflation models from higher-dimensional gauge theories
NASA Astrophysics Data System (ADS)
Furuuchi, Kazuyuki; Koyama, Yoji
2015-02-01
Motivated by the recent detection of B-mode polarization of CMB by BICEP2 which is possibly of primordial origin, we study large field inflation models which can be obtained from higher-dimensional gauge theories. The constraints from CMB observations on the gauge theory parameters are given, and their naturalness are discussed. Among the models analyzed, Dante's Inferno model turns out to be the most preferred model in this framework.
Large field inflation models from higher-dimensional gauge theories
Furuuchi, Kazuyuki; Koyama, Yoji
2015-02-23
Motivated by the recent detection of B-mode polarization of CMB by BICEP2 which is possibly of primordial origin, we study large field inflation models which can be obtained from higher-dimensional gauge theories. The constraints from CMB observations on the gauge theory parameters are given, and their naturalness are discussed. Among the models analyzed, Dante’s Inferno model turns out to be the most preferred model in this framework.
An effective field theory calculation of the ϱ parameter
NASA Astrophysics Data System (ADS)
Cohen, Andrew; Georgi, Howard; Grinstein, Benjamin
1984-01-01
The effective field theory formalism is reviewed. A general algorithm for constructing an effective lagrangian involving only light particles out of a renormalizable theory of light and heavy particles is stated. Strong interaction corrections are easily integrated into the formalism. As an example of its use, corrections Δϱ to the weak interactions ϱ parameter due to heavy particles are studied and the Einhorn-Jones-Veltman conjecture on the positivity of Δϱ is revisited.
Inductive approach towards a phenomenologically more satisfactory unififed field theory
Rayski, J.; Rayski J.M. Jnr.
1985-11-01
A unified field theory constituting a fusion of the ideas of supersymmetries with general relativity and gauge theory is investigated. A Lagrangian formalism is constructed step by step; the last step consists in a marriage with Kaluza's idea of a multidimensional space-time. Our aim is not to achieve a full local supersymmetry in eleven dimensions, but rather to attain a compromise with the symmetries of the fundamental interactions either known phenomenologically, or only suspected to exist in nature.
Planar limit of orientifold field theories and emergent center symmetry
NASA Astrophysics Data System (ADS)
Armoni, Adi; Shifman, Mikhail; Ünsal, Mithat
2008-02-01
We consider orientifold field theories [i.e., SU(N) Yang-Mills theories with fermions in the two-index symmetric or antisymmetric representations] on R3×S1 where the compact dimension can be either temporal or spatial. These theories are planar equivalent to supersymmetric Yang-Mills theory. The latter has ZN center symmetry. The famous Polyakov criterion establishing confinement-deconfinement phase transition as that from ZN symmetric to ZN broken phase applies. At the Lagrangian level the orientifold theories have at most a Z2 center. We discuss how the full ZN center symmetry dynamically emerges in the orientifold theories in the limit N→∞. In the confining phase the manifestation of this enhancement is the existence of stable k strings in the large-N limit of the orientifold theories. These strings are identical to those of supersymmetric Yang-Mills theories. We argue that critical temperatures (and other features) of the confinement-deconfinement phase transition are the same in the orientifold daughters and their supersymmetric parent up to 1/N corrections. We also discuss the Abelian and non-Abelian confining regimes of four-dimensional QCD-like theories.
Planar limit of orientifold field theories and emergent center symmetry
Armoni, Adi; Shifman, Mikhail; Uensal, Mithat
2008-02-15
We consider orientifold field theories [i.e., SU(N) Yang-Mills theories with fermions in the two-index symmetric or antisymmetric representations] on R{sub 3}xS{sub 1} where the compact dimension can be either temporal or spatial. These theories are planar equivalent to supersymmetric Yang-Mills theory. The latter has Z{sub N} center symmetry. The famous Polyakov criterion establishing confinement-deconfinement phase transition as that from Z{sub N} symmetric to Z{sub N} broken phase applies. At the Lagrangian level the orientifold theories have at most a Z{sub 2} center. We discuss how the full Z{sub N} center symmetry dynamically emerges in the orientifold theories in the limit N{yields}{infinity}. In the confining phase the manifestation of this enhancement is the existence of stable k strings in the large-N limit of the orientifold theories. These strings are identical to those of supersymmetric Yang-Mills theories. We argue that critical temperatures (and other features) of the confinement-deconfinement phase transition are the same in the orientifold daughters and their supersymmetric parent up to 1/N corrections. We also discuss the Abelian and non-Abelian confining regimes of four-dimensional QCD-like theories.
Motion of small bodies in classical field theory
Gralla, Samuel E.
2010-04-15
I show how prior work with R. Wald on geodesic motion in general relativity can be generalized to classical field theories of a metric and other tensor fields on four-dimensional spacetime that (1) are second-order and (2) follow from a diffeomorphism-covariant Lagrangian. The approach is to consider a one-parameter-family of solutions to the field equations satisfying certain assumptions designed to reflect the existence of a body whose size, mass, and various charges are simultaneously scaled to zero. (That such solutions exist places a further restriction on the class of theories to which our results apply.) Assumptions are made only on the spacetime region outside of the body, so that the results apply independent of the body's composition (and, e.g., black holes are allowed). The worldline 'left behind' by the shrinking, disappearing body is interpreted as its lowest-order motion. An equation for this worldline follows from the 'Bianchi identity' for the theory, without use of any properties of the field equations beyond their being second-order. The form of the force law for a theory therefore depends only on the ranks of its various tensor fields; the detailed properties of the field equations are relevant only for determining the charges for a particular body (which are the ''monopoles'' of its exterior fields in a suitable limiting sense). I explicitly derive the force law (and mass-evolution law) in the case of scalar and vector fields, and give the recipe in the higher-rank case. Note that the vector force law is quite complicated, simplifying to the Lorentz force law only in the presence of the Maxwell gauge symmetry. Example applications of the results are the motion of 'chameleon' bodies beyond the Newtonian limit, and the motion of bodies in (classical) non-Abelian gauge theory. I also make some comments on the role that scaling plays in the appearance of universality in the motion of bodies.
Nonequilibrium Dynamical Mean-Field Theory for Bosonic Lattice Models
NASA Astrophysics Data System (ADS)
Strand, Hugo U. R.; Eckstein, Martin; Werner, Philipp
2015-01-01
We develop the nonequilibrium extension of bosonic dynamical mean-field theory and a Nambu real-time strong-coupling perturbative impurity solver. In contrast to Gutzwiller mean-field theory and strong-coupling perturbative approaches, nonequilibrium bosonic dynamical mean-field theory captures not only dynamical transitions but also damping and thermalization effects at finite temperature. We apply the formalism to quenches in the Bose-Hubbard model, starting from both the normal and the Bose-condensed phases. Depending on the parameter regime, one observes qualitatively different dynamical properties, such as rapid thermalization, trapping in metastable superfluid or normal states, as well as long-lived or strongly damped amplitude oscillations. We summarize our results in nonequilibrium "phase diagrams" that map out the different dynamical regimes.
Quantum entanglement of local operators in conformal field theories.
Nozaki, Masahiro; Numasawa, Tokiro; Takayanagi, Tadashi
2014-03-21
We introduce a series of quantities which characterize a given local operator in any conformal field theory from the viewpoint of quantum entanglement. It is defined by the increased amount of (Rényi) entanglement entropy at late time for an excited state defined by acting the local operator on the vacuum. We consider a conformal field theory on an infinite space and take the subsystem in the definition of the entanglement entropy to be its half. We calculate these quantities for a free massless scalar field theory in two, four and six dimensions. We find that these results are interpreted in terms of quantum entanglement of a finite number of states, including Einstein-Podolsky-Rosen states. They agree with a heuristic picture of propagations of entangled particles.
Quantum Lifshitz Field Theory of a Frustrated Ferromagnet.
Balents, Leon; Starykh, Oleg A
2016-04-29
We propose a universal nonlinear sigma model field theory for one-dimensional frustrated ferromagnets, which applies in the vicinity of a "quantum Lifshitz point," at which the ferromagnetic state develops a spin wave instability. We investigate the phase diagram resulting from perturbations of the exchange and of magnetic field away from the Lifshitz point, and uncover a rich structure with two distinct regimes of different properties, depending upon the value of a marginal, dimensionless, parameter of the theory. In the regime relevant for one-dimensional systems with low spin, we find a metamagnetic transition line to a vector chiral phase. This line terminates in a critical end point, beyond which there is at least one multipolar or "spin nematic" phase. We show that the field theory is asymptotically exactly soluble near the Lifshitz point.
Differential geometry with a projection: application to double field theory
NASA Astrophysics Data System (ADS)
Jeon, Imtak; Lee, Kanghoon; Park, Jeong-Hyuck
2011-04-01
In recent development of double field theory, as for the description of the massless sector of closed strings, the spacetime dimension is formally doubled, i.e. from D to D+ D, and the T-duality is realized manifestly as a global O( D, D) rotation. In this paper, we conceive a differential geometry characterized by a O( D, D) symmetric projection, as the underlying mathematical structure of double field theory. We introduce a differential operator compatible with the projection, which, contracted with the projection, can be covariantized and may replace the ordinary derivatives in the generalized Lie derivative that generates the gauge symmetry of double field theory. We construct various gauge covariant tensors which include a scalar and a tensor carrying two O( D, D) vector indices.
Clustering properties, Jack polynomials and unitary conformal field theories
NASA Astrophysics Data System (ADS)
Estienne, Benoit; Regnault, Nicolas; Santachiara, Raoul
2010-01-01
Recently, Jack polynomials have been proposed as natural generalizations of Z Read-Rezayi states describing non-Abelian fractional quantum Hall systems. These polynomials are conjectured to be related to correlation functions of a class of W-conformal field theories based on the Lie algebra A. These theories can be considered as non-unitary solutions of a more general series of CFTs with Z symmetry, the parafermionic theories. Starting from the observation that some parafermionic theories admit unitary solutions as well, we show, by computing the corresponding correlation functions, that these theories provide trial wavefunctions which satisfy the same clustering properties as the non-unitary ones. We show explicitly that, although the wavefunctions constructed by unitary CFTs cannot be expressed as a single Jack polynomial, they still show a fine structure where the mathematical properties of the Jack polynomials play a major role.
BPS index and 4d N = 2 superconformal field theories
NASA Astrophysics Data System (ADS)
Sakai, Kazuhiro
2016-07-01
We study the BPS index for the four-dimensional rank-one N = 2 superconformal field theories H 0 , H 1 , H 2 , E 6 , E 7 , E 8. We consider compactifications of the E-string theory on T 2 in which these theories arise as low energy limits. Using this realization we clarify the general structure of the BPS index. The index is characterized by two exponents and a sequence of invariants. We determine the exponents and the first few invariants.
New Phenomena in NC Field Theory and Emergent Spacetime Geometry
Ydri, Badis
2010-10-31
We give a brief review of two nonperturbative phenomena typical of noncommutative field theory which are known to lead to the perturbative instability known as the UV-IR mixing. The first phenomena concerns the emergence/evaporation of spacetime geometry in matrix models which describe perturbative noncommutative gauge theory on fuzzy backgrounds. In particular we show that the transition from a geometrical background to a matrix phase makes the description of noncommutative gauge theory in terms of fields via the Weyl map only valid below a critical value g*. The second phenomena concerns the appearance of a nonuniform ordered phase in noncommutative scalar {phi}{sup 4} field theory and the spontaneous symmetry breaking of translational/rotational invariance which happens even in two dimensions. We argue that this phenomena also originates in the underlying matrix degrees of freedom of the noncommutative field theory. Furthermore it is conjectured that in addition to the usual WF fixed point at {theta} = 0 there must exist a novel fixed point at {theta} = {infinity} corresponding to the quartic hermitian matrix model.
Energy flow in non-equilibrium conformal field theory
NASA Astrophysics Data System (ADS)
Bernard, Denis; Doyon, Benjamin
2012-09-01
We study the energy current and its fluctuations in quantum gapless 1d systems far from equilibrium modeled by conformal field theory, where two separated halves are prepared at distinct temperatures and glued together at a point contact. We prove that these systems converge towards steady states, and give a general description of such non-equilibrium steady states in terms of quantum field theory data. We compute the large deviation function, also called the full counting statistics, of energy transfer through the contact. These are universal and satisfy fluctuation relations. We provide a simple representation of these quantum fluctuations in terms of classical Poisson processes whose intensities are proportional to Boltzmann weights.
Modular Hamiltonian for Excited States in Conformal Field Theory
NASA Astrophysics Data System (ADS)
Lashkari, Nima
2016-07-01
We present a novel replica trick that computes the relative entropy of two arbitrary states in conformal field theory. Our replica trick is based on the analytic continuation of partition functions that break the Zn replica symmetry. It provides a method for computing arbitrary matrix elements of the modular Hamiltonian corresponding to excited states in terms of correlation functions. We show that the quantum Fisher information in vacuum can be expressed in terms of two-point functions on the replica geometry. We perform sample calculations in two-dimensional conformal field theories.
Approaches to the sign problem in lattice field theory
NASA Astrophysics Data System (ADS)
Gattringer, Christof; Langfeld, Kurt
2016-08-01
Quantum field theories (QFTs) at finite densities of matter generically involve complex actions. Standard Monte Carlo simulations based upon importance sampling, which have been producing quantitative first principle results in particle physics for almost forty years, cannot be applied in this case. Various strategies to overcome this so-called sign problem or complex action problem were proposed during the last thirty years. We here review the sign problem in lattice field theories, focusing on two more recent methods: dualization to worldline type of representations and the density-of-states approach.
Modular Hamiltonian for Excited States in Conformal Field Theory.
Lashkari, Nima
2016-07-22
We present a novel replica trick that computes the relative entropy of two arbitrary states in conformal field theory. Our replica trick is based on the analytic continuation of partition functions that break the Z_{n} replica symmetry. It provides a method for computing arbitrary matrix elements of the modular Hamiltonian corresponding to excited states in terms of correlation functions. We show that the quantum Fisher information in vacuum can be expressed in terms of two-point functions on the replica geometry. We perform sample calculations in two-dimensional conformal field theories. PMID:27494465
On the CJT formalism in multi-field theories
NASA Astrophysics Data System (ADS)
Amelino-Camelia, Giovanni
1996-02-01
The issues that arise when using the Cornwall-Jackiw-Tomboulis formalism in multi-field theories are investigated. Particular attention is devoted to the interplay between temperature effects, ultraviolet structure, and the interdependence of the gap equations. Results are presented explicitly in the case of the evaluation of the finite temperature effective potential of a theory with two scalar fields which has attracted interest as a toy model for symmetry nonrestoration at high temperatures. The lowest nontrivial order of approximation of the Cornwall-Jackiw-Tomboulis effective potential is shown to lead to consistent results, which are relevant for recent studies of symmetry nonrestoration by Bimonte and Lozano.
Modular Hamiltonian for Excited States in Conformal Field Theory.
Lashkari, Nima
2016-07-22
We present a novel replica trick that computes the relative entropy of two arbitrary states in conformal field theory. Our replica trick is based on the analytic continuation of partition functions that break the Z_{n} replica symmetry. It provides a method for computing arbitrary matrix elements of the modular Hamiltonian corresponding to excited states in terms of correlation functions. We show that the quantum Fisher information in vacuum can be expressed in terms of two-point functions on the replica geometry. We perform sample calculations in two-dimensional conformal field theories.
A field theory of piezoelectric media containing dislocations
Taupin, V. Fressengeas, C.; Ventura, P.; Lebyodkin, M.
2014-04-14
A field theory is proposed to extend the standard piezoelectric framework for linear elastic solids by accounting for the presence and motion of dislocation fields and assessing their impact on the piezoelectric properties. The proposed theory describes the incompatible lattice distortion and residual piezoelectric polarization fields induced by dislocation ensembles, as well as the dynamic evolution of these fields through dislocation motion driven by coupled electro-mechanical loading. It is suggested that (i) dislocation mobility may be enhanced or inhibited by the electric field, depending on the polarity of the latter, (ii) plasticity mediated by dislocation motion allows capturing long-term time-dependent properties of piezoelectric polarization. Due to the continuity of the proposed electro-mechanical framework, the stress/strain and polarization fields are smooth even in the dislocation core regions. The theory is applied to gallium nitride layers for validation. The piezoelectric polarization fields associated with bulk screw/edge dislocations are retrieved and surface potential modulations are predicted. The results are extended to dislocation loops.
Elliptic Genera of Two-Dimensional Gauge Theories with Rank-One Gauge Groups
NASA Astrophysics Data System (ADS)
Benini, Francesco; Eager, Richard; Hori, Kentaro; Tachikawa, Yuji
2014-04-01
We compute the elliptic genera of two-dimensional and -gauged linear sigma models via supersymmetric localization, for rank-one gauge groups. The elliptic genus is expressed as a sum over residues of a meromorphic function whose argument is the holonomy of the gauge field along both the spatial and the temporal directions of the torus. We illustrate our formulas by a few examples including the quintic Calabi-Yau, SU(2) and O(2) gauge theories coupled to N fundamental chiral multiplets, and a geometric model.
Quantum field theory with a preferred direction: The very special relativity framework
NASA Astrophysics Data System (ADS)
Lee, Cheng-Yang
2016-02-01
The theory of very special relativity (VSR) proposed by Cohen and Glashow contains an intrinsic preferred direction. Starting from the irreducible unitary representation of the inhomogeneous VSR group I S I M (2 ), we present a rigorous construction of quantum field theory with a preferred direction. We find that although the particles and their quantum fields between the VSR and Lorentz sectors are physically different, they share many similarities. The massive spin-half and spin-one vector fields are local and satisfy the Dirac and Proca equations, respectively. This result can be generalized to higher-spin field theories. By studying the Yukawa and standard gauge interactions, we obtain a qualitative understanding on the effects of the preferred direction. Its effect is manifest for polarized processes but are otherwise absent.
Equivalence of emergent de Sitter spaces from conformal field theory
NASA Astrophysics Data System (ADS)
Asplund, Curtis T.; Callebaut, Nele; Zukowski, Claire
2016-09-01
Recently, two groups have made distinct proposals for a de Sitter space that is emergent from conformal field theory (CFT). The first proposal is that, for two-dimensional holographic CFTs, the kinematic space of geodesics on a space-like slice of the asymptotically anti-de Sitter bulk is two-dimensional de Sitter space (dS2), with a metric that can be derived from the entanglement entropy of intervals in the CFT. In the second proposal, de Sitter dynamics emerges naturally from the first law of entanglement entropy for perturbations around the vacuum state of CFTs. We provide support for the equivalence of these two emergent spacetimes in the vacuum case and beyond. In particular, we study the kinematic spaces of nontrivial solutions of 3d gravity, including the BTZ black string, BTZ black hole, and conical singularities. We argue that the resulting spaces are generically globally hyperbolic spacetimes that support dynamics given boundary conditions at future infinity. For the BTZ black string, corresponding to a thermal state of the CFT, we show that both prescriptions lead to an emergent hyperbolic patch of dS2. We offer a general method for relating kinematic space and the auxiliary de Sitter space that is valid in the vacuum and thermal cases.
Planar Limit of Orientifold Field Theories and Emergent Center Symmetry
Armoni, Adi; Shifman, Mikhail; Unsal, Mithat
2007-12-05
We consider orientifold field theories (i.e. SU(N) Yang-Mills theories with fermions in the two-index symmetric or antisymmetric representations) on R{sub 3} x S{sub 1} where the compact dimension can be either temporal or spatial. These theories are planar equivalent to supersymmetric Yang-Mills. The latter has Z{sub N} center symmetry. The famous Polyakov criterion establishing confinement-deconfinement phase transition as that from Z{sub N} symmetric to Z{sub N} broken phase applies. At the Lagrangian level the orientifold theories have at most a Z{sub 2} center. We discuss how the full Z{sub N} center symmetry dynamically emerges in the orientifold theories in the limit N {yields} {infinity}. In the confining phase the manifestation of this enhancement is the existence of stable k-strings in the large-N limit of the orientifold theories. These strings are identical to those of supersymmetric Yang-Mills theories. We argue that critical temperatures (and other features) of the confinement-deconfinement phase transition are the same in the orientifold daughters and their supersymmetric parent up to 1/N corrections. We also discuss the Abelian and non-Abelian confining regimes of four-dimensional QCD-like theories.
N=2, 4 supersymmetric gauge field theory in two-time physics
Bars, Itzhak; Kuo, Y.-C.
2009-01-15
In the context of two-time physics in 4+2 dimensions we construct the most general N=2, 4 supersymmetric Yang-Mills gauge theories for any gauge group G. This builds on our previous work for N=1 supersymmetry (SUSY). The action, the conserved SUSY currents, and the SU(N) covariant SUSY transformation laws are presented for both N=2 and N=4. When the equations of motion are used the SUSY transformations close to the supergroup SU(2,2|N) with N=1, 2, 4. The SU(2,2)=SO(4,2) subsymmetry is realized linearly on 4+2 dimensional flat spacetime. All fields, including vectors and spinors, are in 4+2 dimensions. The extra gauge symmetries in 2T field theory, together with the kinematic constraints that follow from the action, remove all the ghosts to give a unitary theory. By choosing gauges and solving the kinematic equations, the 2T field theory in 4+2 flat spacetime can be reduced to various shadows in various 3+1 dimensional (generally curved) spacetimes. These shadows are related to each other by dualities. The conformal shadows of our theories in flat 3+1 dimensions coincide with the well known counterpart N=1, 2, 4 supersymmetric massless renormalizable field theories in 3+1 dimensions. It is expected that our more symmetric new structures in 4+2 spacetime may be useful for nonperturbative or exact solutions of these theories.
Topological BF field theory description of topological insulators
Cho, Gil Young; Moore, Joel E.
2011-06-15
Research Highlights: > We show that a BF theory is the effective theory of 2D and 3D topological insulators. > The non-gauge-invariance of the bulk theory yields surface terms for a bosonized Dirac fermion. > The 'axion' term in electromagnetism is correctly obtained from gapped surfaces. > Generalizations to possible fractional phases are discussed in closing. - Abstract: Topological phases of matter are described universally by topological field theories in the same way that symmetry-breaking phases of matter are described by Landau-Ginzburg field theories. We propose that topological insulators in two and three dimensions are described by a version of abelian BF theory. For the two-dimensional topological insulator or quantum spin Hall state, this description is essentially equivalent to a pair of Chern-Simons theories, consistent with the realization of this phase as paired integer quantum Hall effect states. The BF description can be motivated from the local excitations produced when a {pi} flux is threaded through this state. For the three-dimensional topological insulator, the BF description is less obvious but quite versatile: it contains a gapless surface Dirac fermion when time-reversal-symmetry is preserved and yields 'axion electrodynamics', i.e., an electromagnetic E . B term, when time-reversal symmetry is broken and the surfaces are gapped. Just as changing the coefficients and charges of 2D Chern-Simons theory allows one to obtain fractional quantum Hall states starting from integer states, BF theory could also describe (at a macroscopic level) fractional 3D topological insulators with fractional statistics of point-like and line-like objects.
Field theory of propagating reaction-diffusion fronts
Escudero, C.
2004-10-01
The problem of velocity selection of reaction-diffusion fronts has been widely investigated. While the mean-field limit results are well known theoretically, there is a lack of analytic progress in those cases in which fluctuations are to be taken into account. Here, we construct an analytic theory connecting the first principles of the reaction-diffusion process to an effective equation of motion via field-theoretic arguments, and we arrive at results already confirmed by numerical simulations.
Visible and Dark Fermions in Multi-Spinor Field Theory
NASA Astrophysics Data System (ADS)
Sogami, Ikuo S.
Why fundamental fermions exist in the modes of three families of quarks and leptons with the color and electroweak gauge symmetry? Is it possible to generalize the Standard Model so as to accommodate some degrees of freedom of dark matter in it? As an attempt to elucidate these basic problems, I have developed a new unified field theory of chiral multi-spinor fields which have three family modes of ordinary quarks and leptons and one additional family of dark quarks and leptons.
Interacting scalar field theory in general curved space-time
Kodaira, J.
1986-05-15
The ultraviolet divergences of two-loop diagrams in general curved space-time are determined for the six-dimensional phi/sup 3/ theory. The background-field method is used to evaluate the effective action. In order to isolate the short-distance singularities, the Feynman propagator is expanded by the heat kernel and dimensional regularization is employed. The gravitational counterterms as well as those for the matter field are explicitly given to the two-loop order.
An effective field theory for forward scattering and factorization violation
NASA Astrophysics Data System (ADS)
Rothstein, Ira Z.; Stewart, Iain W.
2016-08-01
Starting with QCD, we derive an effective field theory description for forward scattering and factorization violation as part of the soft-collinear effective field theory (SCET) for high energy scattering. These phenomena are mediated by long distance Glauber gluon exchanges, which are static in time, localized in the longitudinal distance, and act as a kernel for forward scattering where | t| ≪ s. In hard scattering, Glauber gluons can induce corrections which invalidate factorization. With SCET, Glauber exchange graphs can be calculated explicitly, and are distinct from graphs involving soft, collinear, or ultrasoft gluons. We derive a complete basis of operators which describe the leading power effects of Glauber exchange. Key ingredients include regulating light-cone rapidity singularities and subtractions which prevent double counting. Our results include a novel all orders gauge invariant pure glue soft operator which appears between two collinear rapidity sectors. The 1-gluon Feynman rule for the soft operator coincides with the Lipatov vertex, but it also contributes to emissions with ≥ 2 soft gluons. Our Glauber operator basis is derived using tree level and one-loop matching calculations from full QCD to both SCETII and SCETI. The one-loop amplitude's rapidity renormalization involves mixing of color octet operators and yields gluon Reggeization at the amplitude level. The rapidity renormalization group equation for the leading soft and collinear functions in the forward scattering cross section are each given by the BFKL equation. Various properties of Glauber gluon exchange in the context of both forward scattering and hard scattering factorization are described. For example, we derive an explicit rule for when eikonalization is valid, and provide a direct connection to the picture of multiple Wilson lines crossing a shockwave. In hard scattering operators Glauber subtractions for soft and collinear loop diagrams ensure that we are not sensitive to
Tushev, A V
2006-10-31
In the present paper certain methods are developed that enable one to study the properties of the controller of a prime faithful ideal I of the group algebra kA of an Abelian torsion-free group A of finite rank over a field k. The main idea is that the quotient ring kA/I by the given ideal I can be embedded as an integral domain k[A] into some field F and the group A becomes a subgroup of the multiplicative group of the field F. This allows one to apply certain results of field theory, such as Kummer's theory and the properties of the multiplicative groups of fields, to the study of the integral domain k[A]. In turn, the properties of the integral domain k[A]{approx_equal}kA/I depend essentially on the properties of the ideal I. In particular, by using these methods, an independent proof of the new version of Brookes's theorem on the controllers of prime ideals of the group algebra kA of an Abelian torsion-free group A of finite rank is obtained in the case where the field k has positive characteristic.
Representing the Electromagnetic Field: How Maxwell's Mathematics Empowered Faraday's Field Theory
ERIC Educational Resources Information Center
Tweney, Ryan D.
2011-01-01
James Clerk Maxwell "translated" Michael Faraday's experimentally-based field theory into the mathematical representation now known as "Maxwell's Equations." Working with a variety of mathematical representations and physical models Maxwell extended the reach of Faraday's theory and brought it into consistency with other results in the physics of…
ERIC Educational Resources Information Center
O'Neil, James M.
1998-01-01
Relates Wade's and Gelso's Male Reference Group Dependence Theory to past and present literature in the new psychology of men. Points out the strengths of the ideas and data; reflects on where the theory needs more clarification and extension. (MKA)
The Effective Field Theory Approach to Fluid Dynamics
NASA Astrophysics Data System (ADS)
Endlich, Solomon George Shamsuddin Osman
In this thesis we initiate a systematic study of fluid dynamics using the effective field theory (EFT) program. We consider the canonical quantization of an ordinary fluid in an attempt to discover if there is some kind of quantum mechanical inconsistency with ordinary fluids at zero temperature. The system exhibits a number of peculiarities associated with the vortex degrees of freedom. We also study the dynamics of a nearly incompressible fluid via (classical) effective field theory. In the kinematical regime corresponding to near incompressibility (small fluid velocities and accelerations), compressional modes are, by definition, difficult to excite, and can be dealt with perturbatively. We systematically outline the corresponding perturbative expansion, which can be thought of as an expansion in the ratio of fluid velocity and speed of sound. This perturbation theory allows us to compute many interesting quantities associated with sound-flow interactions. Additionally, we also improve on the so-called vortex filament model, by providing a local field theory describing the dynamics of vortex-line systems and their interaction with sound, to all orders in perturbation theory. Next, we develop a cosmological model where primordial inflation is driven by a 'solid'. The low energy EFT describing such a system is just a less symmetric version of the action of a fluid---it lacks the volume preserving diffeomorphism. The symmetry breaking pattern of this system differs drastically from that of standard inflationary models: time translations are unbroken. This prevents our model from fitting into the standard effective field theory description of adiabatic perturbations, with crucial consequences for the dynamics of cosmological perturbations. And finally, we introduce dissipative effects in the effective field theory of hydrodynamics. We do this in a model-independent fashion by coupling the long-distance degrees of freedom explicitly kept in the effective field theory
Theory of a ring laser. [electromagnetic field and wave equations
NASA Technical Reports Server (NTRS)
Menegozzi, L. N.; Lamb, W. E., Jr.
1973-01-01
Development of a systematic formulation of the theory of a ring laser which is based on first principles and uses a well-known model for laser operation. A simple physical derivation of the electromagnetic field equations for a noninertial reference frame in uniform rotation is presented, and an attempt is made to clarify the nature of the Fox-Li modes for an open polygonal resonator. The polarization of the active medium is obtained by using a Fourier-series method which permits the formulation of a strong-signal theory, and solutions are given in terms of continued fractions. It is shown that when such a continued fraction is expanded to third order in the fields, the familiar small-signal ring-laser theory is obtained.
Effective Field Theory of the Disordered Weyl Semimetal.
Altland, Alexander; Bagrets, Dmitry
2015-06-26
In disordered Weyl semimetals, mechanisms of topological origin lead to the protection against Anderson localization, and at the same time to different types of transverse electromagnetic response-the anomalous Hall and the chiral magnetic effect. We here apply field theory methods to discuss the manifestation of these phenomena at length scales that are beyond the scope of diagrammatic perturbation theory. Specifically, we show how an interplay of symmetry breaking and the chiral anomaly leads to a field theory containing two types of topological terms. Generating the unconventional response coefficients of the system, these terms remain largely unaffected by disorder, i.e., information on the chirality of the system remains visible even at large length scales.
On gradient field theories: gradient magnetostatics and gradient elasticity
NASA Astrophysics Data System (ADS)
Lazar, Markus
2014-09-01
In this work, the fundamentals of gradient field theories are presented and reviewed. In particular, the theories of gradient magnetostatics and gradient elasticity are investigated and compared. For gradient magnetostatics, non-singular expressions for the magnetic vector gauge potential, the Biot-Savart law, the Lorentz force and the mutual interaction energy of two electric current loops are derived and discussed. For gradient elasticity, non-singular forms of all dislocation key formulas (Burgers equation, Mura equation, Peach-Koehler stress equation, Peach-Koehler force equation, and mutual interaction energy of two dislocation loops) are presented. In addition, similarities between an electric current loop and a dislocation loop are pointed out. The obtained fields for both gradient theories are non-singular due to a straightforward and self-consistent regularization.
Geometric and Topological Methods for Quantum Field Theory
NASA Astrophysics Data System (ADS)
Cardona, Alexander; Contreras, Iván.; Reyes-Lega, Andrés. F.
2013-05-01
Introduction; 1. A brief introduction to Dirac manifolds Henrique Bursztyn; 2. Differential geometry of holomorphic vector bundles on a curve Florent Schaffhauser; 3. Paths towards an extension of Chern-Weil calculus to a class of infinite dimensional vector bundles Sylvie Paycha; 4. Introduction to Feynman integrals Stefan Weinzierl; 5. Iterated integrals in quantum field theory Francis Brown; 6. Geometric issues in quantum field theory and string theory Luis J. Boya; 7. Geometric aspects of the standard model and the mysteries of matter Florian Scheck; 8. Absence of singular continuous spectrum for some geometric Laplacians Leonardo A. Cano García; 9. Models for formal groupoids Iván Contreras; 10. Elliptic PDEs and smoothness of weakly Einstein metrics of Hölder regularity Andrés Vargas; 11. Regularized traces and the index formula for manifolds with boundary Alexander Cardona and César Del Corral; Index.
Scalar field theory in the strong self-interaction limit
NASA Astrophysics Data System (ADS)
Frasca, Marco
2014-06-01
The Standard Model with a classical conformal invariance holds the promise to lead to a better understanding of the hierarchy problem and could pave the way beyond the Standard Model physics. Thus, we give here a mathematical treatment of a massless quartic scalar field theory with a strong self-coupling both classically and for quantum field theory. We use a set of classical solutions recently found and show that there exist an infinite set of infrared trivial scalar theories with a mass gap. Free particles have superimposed a harmonic oscillator set of states. The classical solution is displayed through a current expansion and the next-to-leading order quantum correction is provided. Application to the Standard Model would entail the existence of higher excited states of the Higgs particle and reduced decay rates to WW and ZZ that could already be measured.
The effective field theory of K-mouflage
Brax, Philippe; Valageas, Patrick E-mail: patrick.valageas@cea.fr
2016-01-01
We describe K-mouflage models of modified gravity using the effective field theory of dark energy. We show how the Lagrangian density K defining the K-mouflage models appears in the effective field theory framework, at both the exact fully nonlinear level and at the quadratic order of the effective action. We find that K-mouflage scenarios only generate the operator (δg{sup 00}{sub (u)}){sup n} at each order n. We also reverse engineer K-mouflage models by reconstructing the whole effective field theory, and the full cosmological behaviour, from two functions of the Jordan-frame scale factor in a tomographic manner. This parameterisation is directly related to the implementation of the K-mouflage screening mechanism: screening occurs when K' is large in a dense environment such as the deep matter and radiation eras. In this way, K-mouflage can be easily implemented as a calculable subclass of models described by the effective field theory of dark energy which could be probed by future surveys.
On the exotic Higgs decays in effective field theory
NASA Astrophysics Data System (ADS)
Bélusca-Maïto, Hermès; Falkowski, Adam
2016-09-01
We discuss exotic Higgs decays in an effective field theory where the Standard Model is extended by dimension-6 operators. We review and update the status of two-body lepton- and quark-flavor-violating decays involving the Higgs boson. We also comment on the possibility of observing three-body flavor-violating Higgs decays in this context.
Holography and hydrodynamics for EMD theory with two Maxwell fields
NASA Astrophysics Data System (ADS)
Smolic, Milena
2013-03-01
We use `generalized dimensional reduction' to relate a specific Einstein-Max-well-Dilaton (EMD) theory, including two gauge fields, three neutral scalars and an axion, to higher-dimensional AdS gravity (with no higher-dimensional Maxwell field). In general, this is a dimensional reduction over compact Einstein spaces in which the dimension of the compact space is continued to non-integral values. Specifically, we perform a non-diagonal Kaluza-Klein (KK) reduction over a torus, involving two KK gauge fields. Our aim is to determine the holographic dictionary and hydrodynamic behaviour of the lower-dimensional theory by performing the generalized dimensional reduction on AdS. We study a specific example of a black brane carrying a wave, whose universal sector is described by gravity coupled to two Maxwell fields, three neutral scalars and an axion, and compute the first order transport coefficients of the dual theory. In these theories {{widehat{ζ}}_s}/widehat{η}<2( {1/( {d-1} )-widehat{c}_s^2} ) , where {{widehat{c}}_s} is the speed of sound, violating a conjectured bound, but an alternative bound is satisfied.
Dynamical mean-field theory from a quantum chemical perspective.
Zgid, Dominika; Chan, Garnet Kin-Lic
2011-03-01
We investigate the dynamical mean-field theory (DMFT) from a quantum chemical perspective. Dynamical mean-field theory offers a formalism to extend quantum chemical methods for finite systems to infinite periodic problems within a local correlation approximation. In addition, quantum chemical techniques can be used to construct new ab initio Hamiltonians and impurity solvers for DMFT. Here, we explore some ways in which these things may be achieved. First, we present an informal overview of dynamical mean-field theory to connect to quantum chemical language. Next, we describe an implementation of dynamical mean-field theory where we start from an ab initio Hartree-Fock Hamiltonian that avoids double counting issues present in many applications of DMFT. We then explore the use of the configuration interaction hierarchy in DMFT as an approximate solver for the impurity problem. We also investigate some numerical issues of convergence within DMFT. Our studies are carried out in the context of the cubic hydrogen model, a simple but challenging test for correlation methods. Finally, we finish with some conclusions for future directions.
An alternative topological field theory of generalized complex geometry
NASA Astrophysics Data System (ADS)
Ikeda, Noriaki; Tokunaga, Tatsuya
2007-09-01
We propose a new topological field theory on generalized complex geometry in two dimension using AKSZ formulation. Zucchini's model is A model in the case that the generalized complex structure depends on only a symplectic structure. Our new model is B model in the case that the generalized complex structure depends on only a complex structure.
Notes on orientifolds of rational conformal field theories
NASA Astrophysics Data System (ADS)
Brunner, Ilka; Hori, Kentaro
2004-07-01
We review and develop the construction of crosscap states associated with parity symmetries in rational conformal field theories. A general method to construct crosscap states in abelian orbifold models is presented. It is then applied to rational U(1) and parafermion systems, where in addition we study the geometrical interpretation of the corresponding parities.
A note on large gauge transformations in double field theory
NASA Astrophysics Data System (ADS)
Naseer, Usman
2015-06-01
We give a detailed proof of the conjecture by Hohm and Zwiebach in double field theory. This result implies that their proposal for large gauge transformations in terms of the Jacobian matrix for coordinate transformations is, as required, equivalent to the standard exponential map associated with the generalized Lie derivative along a suitable parameter.
Schr"odinger's Unified Field Theory: Physics by Public Relations
NASA Astrophysics Data System (ADS)
Halpern, Paul
2009-05-01
We will explore the circumstances surrounding Erwin Schr"odinger's announcement in January 1947 that he had developed a comprehensive unified field theory of gravitation and electromagnetism. We will speculate on Schr"odinger's motivations for the mode and tone of his statements, consider the reaction of the international press within the context of the postwar era, and examine Einstein's response.
When Group Membership Gets Personal: A Theory of Identity Fusion
ERIC Educational Resources Information Center
Swann, William B., Jr.; Jetten, Jolanda; Gomez, Angel; Whitehouse, Harvey; Bastian, Brock
2012-01-01
Identity fusion is a relatively unexplored form of alignment with groups that entails a visceral feeling of oneness with the group. This feeling is associated with unusually porous, highly permeable borders between the personal and social self. These porous borders encourage people to channel their personal agency into group behavior, raising the…
PyR@TE. Renormalization group equations for general gauge theories
NASA Astrophysics Data System (ADS)
Lyonnet, F.; Schienbein, I.; Staub, F.; Wingerter, A.
2014-03-01
Although the two-loop renormalization group equations for a general gauge field theory have been known for quite some time, deriving them for specific models has often been difficult in practice. This is mainly due to the fact that, albeit straightforward, the involved calculations are quite long, tedious and prone to error. The present work is an attempt to facilitate the practical use of the renormalization group equations in model building. To that end, we have developed two completely independent sets of programs written in Python and Mathematica, respectively. The Mathematica scripts will be part of an upcoming release of SARAH 4. The present article describes the collection of Python routines that we dubbed PyR@TE which is an acronym for “Python Renormalization group equations At Two-loop for Everyone”. In PyR@TE, once the user specifies the gauge group and the particle content of the model, the routines automatically generate the full two-loop renormalization group equations for all (dimensionless and dimensionful) parameters. The results can optionally be exported to LaTeX and Mathematica, or stored in a Python data structure for further processing by other programs. For ease of use, we have implemented an interactive mode for PyR@TE in form of an IPython Notebook. As a first application, we have generated with PyR@TE the renormalization group equations for several non-supersymmetric extensions of the Standard Model and found some discrepancies with the existing literature. Catalogue identifier: AERV_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AERV_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 924959 No. of bytes in distributed program, including test data, etc.: 495197 Distribution format: tar.gz Programming language: Python. Computer
Generalized Lee-Wick formulation from higher derivative field theories
Cho, Inyong; Kwon, O-Kab
2010-07-15
We study a higher derivative (HD) field theory with an arbitrary order of derivative for a real scalar field. The degree of freedom for the HD field can be converted to multiple fields with canonical kinetic terms up to the overall sign. The Lagrangian describing the dynamics of the multiple fields is known as the Lee-Wick (LW) form. The first step to obtain the LW form for a given HD Lagrangian is to find an auxiliary field (AF) Lagrangian which is equivalent to the original HD Lagrangian up to the quantum level. Until now, the AF Lagrangian has been studied only for N=2 and 3 cases, where N is the number of poles of the two-point function of the HD scalar field. We construct the AF Lagrangian for arbitrary N. By the linear combinations of AF fields, we also obtain the corresponding LW form. We find the explicit mapping matrices among the HD fields, the AF fields, and the LW fields. As an exercise of our construction, we calculate the relations among parameters and mapping matrices for N=2, 3, and 4 cases.
Massive basketball diagram for a thermal scalar field theory
Andersen, Jens O.; Braaten, Eric; Strickland, Michael
2000-08-15
The ''basketball diagram'' is a three-loop vacuum diagram for a scalar field theory that cannot be expressed in terms of one-loop diagrams. We calculate this diagram for a massive scalar field at nonzero temperature, reducing it to expressions involving three-dimensional integrals that can be easily evaluated numerically. We use this result to calculate the free energy for a massive scalar field with a {phi}{sup 4} interaction to three-loop order. (c) 2000 The American Physical Society.
Radiative self-interaction in classical field theory
NASA Astrophysics Data System (ADS)
Kalman, P.
The products of mass renormalization in an electromagnetic field were studied in order to construct a classical theory of radiative self-interaction. A constraint was applied to the solution of the Dirac equation to ensure that the rest mass contained an electromagnetic component. The level shifts and decay rates of field states were calculated according to the method of Feynman (1961), and the results are discussed. Some applications of the theoretical results in the fields of laser physics and nonlinear optics are considered.
Inflationary solutions in the nonminimally coupled scalar field theory
NASA Astrophysics Data System (ADS)
Koh, Seoktae; Kim, Sang Pyo; Song, Doo Jong
2005-08-01
We study analytically and numerically the inflationary solutions for various type scalar potentials in the nonminimally coupled scalar field theory. The Hamilton-Jacobi equation is used to deal with nonlinear evolutions of inhomogeneous spacetimes and the long-wavelength approximation is employed to find the homogeneous solutions during an inflation period. The constraints that lead to a sufficient number of e-folds, a necessary condition for inflation, are found for the nonminimal coupling constant and initial conditions of the scalar field for inflation potentials. In particular, we numerically find an inflationary solution in the new inflation model of a nonminimal scalar field.
Conformal field theories with infinitely many conservation laws
NASA Astrophysics Data System (ADS)
Todorov, Ivan
2013-02-01
Globally conformal invariant quantum field theories in a D-dimensional space-time (D even) have rational correlation functions and admit an infinite number of conserved (symmetric traceless) tensor currents. In a theory of a scalar field of dimension D-2 they were demonstrated to be generated by bilocal normal products of free massless scalar fields with an O(N), U(N), or Sp(2N) (global) gauge symmetry [B. Bakalov, N. M. Nikolov, K.-H. Rehren, and I. Todorov, "Unitary positive energy representations of scalar bilocal fields," Commun. Math. Phys. 271, 223-246 (2007), 10.1007/s00220-006-0182-2; e-print arXiv:math-ph/0604069v3; B. Bakalov, N. M. Nikolov, K.-H. Rehren, and I. Todorov, "Infinite dimensional Lie algebras in 4D conformal quantum field theory," J. Phys. A Math Theor. 41, 194002 (2008), 10.1088/1751-8113/41/19/194002; e-print arXiv:0711.0627v2 [hep-th
Reconstructing inflationary paradigm within Effective Field Theory framework
NASA Astrophysics Data System (ADS)
Choudhury, Sayantan
2016-03-01
In this paper my prime objective is to analyse the constraints on a sub-Planckian excursion of a single inflaton field within Effective Field Theory framework in a model independent fashion. For a generic single field inflationary potential, using the various parameterization of the primordial power spectrum I have derived the most general expression for the field excursion in terms of various inflationary observables, applying the observational constraints obtained from recent Planck 2015 and Planck 2015 + BICEP2/Keck Array data. By explicit computation I have reconstructed the structural form of the inflationary potential by constraining the Taylor expansion co-efficients appearing in the generic expansion of the potential within the Effective Field Theory. Next I have explicitly derived, a set of higher order inflationary consistency relationships, which would help us to break the degeneracy between various class of inflationary models by differentiating them. I also provided two simple examples of Effective Theory of inflation- inflection-point model and saddle-point model to check the compatibility of the prescribed methodology in the light of Planck 2015 and Planck 2015 + BICEP2/Keck Array data. Finally, I have also checked the validity of the prescription by estimating the cosmological parameters and fitting the theoretical CMB TT, TE and EE angular power spectra with the observed data within the multipole range 2 < l < 2500.
When group membership gets personal: a theory of identity fusion.
Swann, William B; Jetten, Jolanda; Gómez, Angel; Whitehouse, Harvey; Bastian, Brock
2012-07-01
Identity fusion is a relatively unexplored form of alignment with groups that entails a visceral feeling of oneness with the group. This feeling is associated with unusually porous, highly permeable borders between the personal and social self. These porous borders encourage people to channel their personal agency into group behavior, raising the possibility that the personal and social self will combine synergistically to motivate pro-group behavior. Furthermore, the strong personal as well as social identities possessed by highly fused persons cause them to recognize other group members not merely as members of the group but also as unique individuals, prompting the development of strong relational as well as collective ties within the group. In local fusion, people develop relational ties to members of relatively small groups (e.g., families or work teams) with whom they have personal relationships. In extended fusion, people project relational ties onto relatively large collectives composed of many individuals with whom they may have no personal relationships. The research literature indicates that measures of fusion are exceptionally strong predictors of extreme pro-group behavior. Moreover, fusion effects are amplified by augmenting individual agency, either directly (by increasing physiological arousal) or indirectly (by activating personal or social identities). The effects of fusion on pro-group actions are mediated by perceptions of arousal and invulnerability. Possible causes of identity fusion--ranging from relatively distal, evolutionary, and cultural influences to more proximal, contextual influences--are discussed. Finally, implications and future directions are considered. PMID:22642548
Topologically stratified energy minimizers in a product Abelian field theory
NASA Astrophysics Data System (ADS)
Han, Xiaosen; Yang, Yisong
2015-09-01
We study a recently developed product Abelian gauge field theory by Tong and Wong hosting magnetic impurities. We first obtain a necessary and sufficient condition for the existence of a unique solution realizing such impurities in the form of multiple vortices. We next reformulate the theory into an extended model that allows the coexistence of vortices and anti-vortices. The two Abelian gauge fields in the model induce two species of magnetic vortex-lines resulting from Ns vortices and Ps anti-vortices (s = 1, 2) realized as the zeros and poles of two complex-valued Higgs fields, respectively. An existence theorem is established for the governing equations over a compact Riemann surface S which states that a solution with prescribed N1, N2 vortices and P1, P2 anti-vortices of two designated species exists if and only if the inequalities
Quantum field theory for condensation of bosons and fermions
De Souza, Adriano N.; Filho, Victo S.
2013-03-25
In this brief review, we describe the formalism of the quantum field theory for the analysis of the condensation phenomenon in bosonic systems, by considering the cases widely verified in laboratory of trapped gases as condensate states, either with attractive or with repulsive two-body interactions. We review the mathematical formulation of the quantum field theory for many particles in the mean-field approximation, by adopting contact interaction potential. We also describe the phenomenon of condensation in the case of fermions or the degenerate Fermi gas, also verified in laboratory in the crossover BEC-BCS limit. We explain that such a phenomenon, equivalent to the bosonic condensation, can only occur if we consider the coupling of particles in pairs behaving like bosons, as occurs in the case of Cooper's pairs in superconductivity.
Entanglement of Low-Energy Excitations in Conformal Field Theory
Alcaraz, Francisco Castilho; Ibanez Berganza, Miguel; Sierra, German
2011-05-20
In a quantum critical chain, the scaling regime of the energy and momentum of the ground state and low-lying excitations are described by conformal field theory (CFT). The same holds true for the von Neumann and Renyi entropies of the ground state, which display a universal logarithmic behavior depending on the central charge. In this Letter we generalize this result to those excited states of the chain that correspond to primary fields in CFT. It is shown that the nth Renyi entropy is related to a 2n-point correlator of primary fields. We verify this statement for the critical XX and XXZ chains. This result uncovers a new link between quantum information theory and CFT.
Tensor hierarchy and generalized Cartan calculus in SL(3) × SL(2) exceptional field theory
NASA Astrophysics Data System (ADS)
Hohm, Olaf; Wang, Yi-Nan
2015-04-01
We construct exceptional field theory for the duality group SL(3) × SL(2). The theory is defined on a space with 8 `external' coordinates and 6 `internal' coordinates in the (3, 2) fundamental representation, leading to a 14-dimensional generalized spacetime. The bosonic theory is uniquely determined by gauge invariance under generalized external and internal diffeomorphisms. The latter invariance can be made manifest by introducing higher form gauge fields and a so-called tensor hierarchy, which we systematically develop to much higher degree than in previous studies. To this end we introduce a novel Cartan-like tensor calculus based on a covariant nil-potent differential, generalizing the exterior derivative of conventional differential geometry. The theory encodes the full D = 11 or type IIB supergravity, respectively.
Theories in Developing Oral Communication for Specific Learner Group
ERIC Educational Resources Information Center
Hadi, Marham Jupri
2016-01-01
The current article presents some key theories most relevant to the development of oral communication skills in an Indonesian senior high school. Critical analysis on the learners' background is employed to figure out their strengths and weaknesses. The brief overview of the learning context and learners' characteristic are used to identify which…
Kriz, Igor; Loebl, Martin; Somberg, Petr
2013-05-15
We study various mathematical aspects of discrete models on graphs, specifically the Dimer and the Ising models. We focus on proving gluing formulas for individual summands of the partition function. We also obtain partial results regarding conjectured limits realized by fermions in rational conformal field theories.
OPE convergence in non-relativistic conformal field theories
NASA Astrophysics Data System (ADS)
Goldberger, Walter D.; Khandker, Zuhair U.; Prabhu, Siddharth
2015-12-01
Motivated by applications to the study of ultracold atomic gases near the unitarity limit, we investigate the structure of the operator product expansion (OPE) in non-relativistic conformal field theories (NRCFTs). The main tool used in our analysis is the representation theory of charged (i.e. non-zero particle number) operators in the NR-CFT, in particular the mapping between operators and states in a non-relativistic "radial quantization" Hilbert space. Our results include: a determination of the OPE coefficients of descendant operators in terms of those of the underlying primary state, a demonstration of convergence of the (imaginary time) OPE in certain kinematic limits, and an estimate of the decay rate of the OPE tail inside matrix elements which, as in relativistic CFTs, depends exponentially on operator dimensions. To illustrate our results we consider several examples, including a strongly interacting field theory of bosons tuned to the unitarity limit, as well as a class of holographic models. Given the similarity with known statements about the OPE in SO(2, d) invariant field theories, our results suggest the existence of a bootstrap approach to constraining NRCFTs, with applications to bound state spectra and interactions. We briefly comment on a possible implementation of this non-relativistic conformal bootstrap program.
A tracer-kinetic field theory for medical imaging.
Sourbron, Steven
2014-04-01
Dynamic imaging data are currently analyzed with a tracer-kinetic theory developed for individual time curves measured over whole organs. The assumption is that voxels represent isolated systems which all receive indicator through the same arterial inlet. This leads to well-known systematic errors, but also fails to exploit the spatial structure of the data. In this study, a more general theoretical framework is developed which makes full use of the specific structure of image data. The theory encodes the fact that voxels receive indicator from their immediate neighbors rather than from an upstream arterial input. This results in a tracer-kinetic field theory where the tissue parameters are functions of space which can be measured by analyzing the temporal and spatial patterns in the concentrations. The implications are evaluated through a number of field models for common tissue types. The key benefits of a tracer-kinetic field theory are that: 1) long-standing systematic errors can be corrected, specifically the issue of bolus dispersion and the contamination of large-vessel blood flow on tissue perfusion measurements; 2) additional tissue parameters can be measured that characterize convective or diffusive exchange between voxels; 3) the need to measure a separate arterial input function can be eliminated.
Gravitation: Field theory par excellence Newton, Einstein, and beyond
Yilmaz, H.
1984-09-01
Newtonian gravity satifies the two principles of equivalence m/sub i/ = m/sub p/ (the passive principle) and m/sub a/ = m/sub p/ (the active principle). A relativistic gauge field concept in D = s+1 dimensional curved-space will, in general, violate these two principles as in m/sub p/ = ..cap alpha..m/sub i/, m/sub a/ = lambdam/sub p/ where ..cap alpha.. = D: 3 and lambda measures the presence of the field stress-energy t/sup ..nu..//sub ..mu../ in the field equations. It is shown that ..cap alpha.. = 1, lambda = 0 corresponds to general relativity and ..cap alpha.. = 1, lambda = 1 to the theory of the author. It is noted that the correspondence limit of general relativity is not Newton's theory but a theory suggested by Robert Hooke a few years before Newton published his in Principia. The gauge is independent of the two principles but had to do with local special relativistic correspondence and compatibility with quantum mechanics. It is shown that unless ..cap alpha.. = 1, lambda = 1 the generalized theory cannot predict correctly many observables effects, including the 532'' per century Newtonian part in Mercury's perihelion advance.
Double metric, generalized metric, and α' -deformed double field theory
NASA Astrophysics Data System (ADS)
Hohm, Olaf; Zwiebach, Barton
2016-03-01
We relate the unconstrained "double metric" of the "α' -geometry" formulation of double field theory to the constrained generalized metric encoding the spacetime metric and b -field. This is achieved by integrating out auxiliary field components of the double metric in an iterative procedure that induces an infinite number of higher-derivative corrections. As an application, we prove that, to first order in α' and to all orders in fields, the deformed gauge transformations are Green-Schwarz-deformed diffeomorphisms. We also prove that to first order in α' the spacetime action encodes precisely the Green-Schwarz deformation with Chern-Simons forms based on the torsionless gravitational connection. This seems to be in tension with suggestions in the literature that T-duality requires a torsionful connection, but we explain that these assertions are ambiguous since actions that use different connections are related by field redefinitions.
Axiomatics of Galileo-invariant quantum field theory
Dadashev, L.A.
1986-03-01
The aim of this paper is to construct the axiomatics of Galileo-invariant quantum field theory. The importance of this problem is demonstrated from various points of view: general properties that the fields and observables must satisfy are considered; S-matrix nontriviality of one such model is proved; and the differences from the relativistic case are discussed. The proposed system of axioms is in many respects analogous to Wightman axiomatics, but is less general. The main result is contained in theorems which describe the admissible set of initial fields and total Hamiltonians, i.e., precisely the two entities that completely determine interacting fields. The author considers fields that prove the independence of some axioms.
Effective field theory analysis of the self-interacting chameleon
NASA Astrophysics Data System (ADS)
Sanctuary, Hillary; Sturani, Riccardo
2010-08-01
We analyse the phenomenology of a self-interacting scalar field in the context of the chameleon scenario originally proposed by Khoury and Weltman. In the absence of self-interactions, this type of scalar field can mediate long range interactions and simultaneously evade constraints from violation of the weak equivalence principle. By applying to such a scalar field the effective field theory method proposed for Einstein gravity by Goldberger and Rothstein, we give a thorough perturbative evaluation of the importance of non-derivative self-interactions in determining the strength of the chameleon mediated force in the case of orbital motion. The self-interactions are potentially dangerous as they can change the long range behaviour of the field. Nevertheless, we show that they do not lead to any dramatic phenomenological consequence with respect to the linear case and solar system constraints are fulfilled.
Towards Noncommutative Topological Quantum Field Theory: New invariants for 3-manifolds
NASA Astrophysics Data System (ADS)
Zois, I. P.
2016-08-01
We present some ideas for a possible Noncommutative Topological Quantum Field Theory (NCTQFT for short) and Noncommutative Floer Homology (NCFH for short). Our motivation is two-fold and it comes both from physics and mathematics: On the one hand we argue that NCTQFT is the correct mathematical framework for a quantum field theory of all known interactions in nature (including gravity). On the other hand we hope that a possible NCFH will apply to practically every 3-manifold (and not only to homology 3-spheres as ordinary Floer Homology currently does). The two motivations are closely related since, at least in the commutative case, Floer Homology Groups constitute the space of quantum observables of (3+1)-dim Topological Quantum Field Theory. Towards this goal we define some new invariants for 3-manifolds using the space of taut codim-1 foliations modulo coarse isotopy along with various techniques from noncommutative geometry.
Fu, Dong
2006-10-01
An equation of state (EOS) applicable for both the uniform and nonuniform fluids is established by using the density-gradient theory (DGT). In the bulk phases, the EOS reduces to statistical associating fluid theory (SAFT). By combining the EOS with the renormalization group theory (RGT), the vapor-liquid-phase equilibria and surface tensions for 10 nonpolar chainlike fluids are investigated from low temperature up to the critical point. The obtained results agree well with the experimental data.
Nuclear axial currents in chiral effective field theory
Baroni, Alessandro; Girlanda, Luca; Pastore, Saori; Schiavilla, Rocco; Viviani, Michele
2016-01-11
Two-nucleon axial charge and current operators are derived in chiral effective field theory up to one loop. The derivation is based on time-ordered perturbation theory and accounts for cancellations between the contributions of irreducible diagrams and the contributions owing to nonstatic corrections from energy denominators of reducible diagrams. Ultraviolet divergencies associated with the loop corrections are isolated in dimensional regularization. The resulting axial current is finite and conserved in the chiral limit, while the axial charge requires renormalization. As a result, a complete set of contact terms for the axial charge up to the relevant order in the power countingmore » is constructed.« less
Large N correlation functions in superconformal field theories
NASA Astrophysics Data System (ADS)
Rodriguez-Gomez, Diego; Russo, Jorge G.
2016-06-01
We compute correlation functions of chiral primary operators in mathcal{N}=2 super-conformal theories at large N using a construction based on supersymmetric localization recently developed by Gerchkovitz et al. We focus on mathcal{N}=4 SYM as well as on supercon-formal QCD. In the case of mathcal{N}=4 we recover the free field theory results as expected due to non-renormalization theorems. In the case of superconformal QCD we study the planar expansion in the large N limit. The final correlators admit a simple generalization to a finite N formula which exactly matches the various small N results in the literature.
Heavy dark matter annihilation from effective field theory.
Ovanesyan, Grigory; Slatyer, Tracy R; Stewart, Iain W
2015-05-29
We formulate an effective field theory description for SU(2)_{L} triplet fermionic dark matter by combining nonrelativistic dark matter with gauge bosons in the soft-collinear effective theory. For a given dark matter mass, the annihilation cross section to line photons is obtained with 5% precision by simultaneously including Sommerfeld enhancement and the resummation of electroweak Sudakov logarithms at next-to-leading logarithmic order. Using these results, we present more accurate and precise predictions for the gamma-ray line signal from annihilation, updating both existing constraints and the reach of future experiments.
Stationary axisymmetric fields in a teleparallel theory of gravitation
NASA Astrophysics Data System (ADS)
Saez, D.
1984-12-01
The stationary axisymmetric field in the tetrad theory of gravitation of Moller (1978) and hence (as shown by Meyre, 1982) in the teleparallel limit of the gauge theory of Hehl et al. (1978) is investigated analytically. A set of tetrads satisfying the Moller equations and giving a Kerr metric is defined, and its existence is proved. It is suggested that the introduction of suitable conditions could reduce the number of tetrads in the Kerr case to one or a small number, and that the present analytical techniques could be applied to other stationary axisymmetric metrics of general relativity.
Note on Stochastic Quantization of Field Theories with Bottomless Actions
NASA Astrophysics Data System (ADS)
Ito, M.; Morita, K.
1993-07-01
It is shown that the kerneled Langevin equation, which has recently been proposed by Tanaka et al. to quantize field theories with bottomless actions, reproduces perturbation theory results independent of the initial conditions. The effective potential is approximately determined from the kerneled Langevin equation to be bounded from below. The evolution equation for the two-point correlation function also defines the effective potential for the propagator, which is given for the zero-dimensional ``wrong-sign'' -λφ4 model under the assumption that all higher-moment cumulants than the second vanish.
Motion of small bodies in classical field theory
NASA Astrophysics Data System (ADS)
Gralla, Samuel E.
2010-04-01
I show how prior work with R. Wald on geodesic motion in general relativity can be generalized to classical field theories of a metric and other tensor fields on four-dimensional spacetime that (1) are second-order and (2) follow from a diffeomorphism-covariant Lagrangian. The approach is to consider a one-parameter-family of solutions to the field equations satisfying certain assumptions designed to reflect the existence of a body whose size, mass, and various charges are simultaneously scaled to zero. (That such solutions exist places a further restriction on the class of theories to which our results apply.) Assumptions are made only on the spacetime region outside of the body, so that the results apply independent of the body’s composition (and, e.g., black holes are allowed). The worldline “left behind” by the shrinking, disappearing body is interpreted as its lowest-order motion. An equation for this worldline follows from the “Bianchi identity” for the theory, without use of any properties of the field equations beyond their being second-order. The form of the force law for a theory therefore depends only on the ranks of its various tensor fields; the detailed properties of the field equations are relevant only for determining the charges for a particular body (which are the “monopoles” of its exterior fields in a suitable limiting sense). I explicitly derive the force law (and mass-evolution law) in the case of scalar and vector fields, and give the recipe in the higher-rank case. Note that the vector force law is quite complicated, simplifying to the Lorentz force law only in the presence of the Maxwell gauge symmetry. Example applications of the results are the motion of “chameleon” bodies beyond the Newtonian limit, and the motion of bodies in (classical) non-Abelian gauge theory. I also make some comments on the role that scaling plays in the appearance of universality in the motion of bodies.
The quantum field theory of electric and magnetic charge
NASA Astrophysics Data System (ADS)
Blagojević, M.; Senjanović, P.
1988-01-01
The dynamics of monopoles as quantum objects is described by the quantum field theory of monopoles and charges. Owing to the presence of a preferred direction n, this is the first example of a theory which is not manifestly Lorentz invariant, though intrinsically it possesses this invariance. Another unusual property of this Abelian theory is that it has two coupling constants connected via the quatization condition. The investigation of the basic properties of the theory is facilitated by the existence of various formulations. Thus, Lorentz invariance, which is not easily seen in Schwinger's Hamiltonian framework, is transparent after the introduction of the particle-path representation of Zwanziger's local Langrarian formulation. Ultraviolet properties of the theory receive a superior, n-independent treatment in this representation, with the result that favors opposite renormalization of electric and magnetic charge. The physical content of infrared regularization is clearly described in the one-potential formulation. Several other topics are treated: Dirac's quantum mechanics of the monopole, connection with non-Abelian monopoles, a supersymmetric generalization of the theory, and its possible role in preon dynamics.
Dynamics of N = 4 supersymmetric field theories in 2 + 1 dimensions and their gravity dual
NASA Astrophysics Data System (ADS)
Cottrell, William; Hanson, James; Hashimoto, Akikazu
2016-07-01
In this note we consider N = 4 SYM theories in 2 + 1 dimensions with gauge group U( N ) × U( M ) and k hypermultiplets charged under the U( N ). When k > 2( N - M ), the theory flows to a superconformal fixed point in the IR. Theories with k < 2( N - M ), on the other hand, flows to strong coupling. We explore these theories from the perspective of gravity dual. We find that the gravity duals of theories with k < ( N - M ) contain enhancons even in situations where repulson singularities are absent. We argue that supergravity description is unreliable in the region near these enhancon points. Instead, we show how to construct reliable sugra duals to particular points on the Coulomb branch where the enhancon is screened. We explore how these singularities reappear as one moves around in Coulomb branch and comment on possible field theory interpretation of this phenomenon. In analyzing gauge/gravity duality for these models, we encountered one unexpected surprise, that the condition for the supergravity solution to be reliable and supersymmetric is somewhat weaker than the expectation from field theory. We also discuss similar issues for theories with k = 0.
Einstein-aether theory with a Maxwell field: General formalism
Balakin, Alexander B.; Lemos, José P.S.
2014-11-15
We extend the Einstein-aether theory to include the Maxwell field in a nontrivial manner by taking into account its interaction with the time-like unit vector field characterizing the aether. We also include a generic matter term. We present a model with a Lagrangian that includes cross-terms linear and quadratic in the Maxwell tensor, linear and quadratic in the covariant derivative of the aether velocity four-vector, linear in its second covariant derivative and in the Riemann tensor. We decompose these terms with respect to the irreducible parts of the covariant derivative of the aether velocity, namely, the acceleration four-vector, the shear and vorticity tensors, and the expansion scalar. Furthermore, we discuss the influence of an aether non-uniform motion on the polarization and magnetization of the matter in such an aether environment, as well as on its dielectric and magnetic properties. The total self-consistent system of equations for the electromagnetic and the gravitational fields, and the dynamic equations for the unit vector aether field are obtained. Possible applications of this system are discussed. Based on the principles of effective field theories, we display in an appendix all the terms up to fourth order in derivative operators that can be considered in a Lagrangian that includes the metric, the electromagnetic and the aether fields.
A theory of leadership in human cooperative groups.
Hooper, Paul L; Kaplan, Hillard S; Boone, James L
2010-08-21
Two types of models aim to account the origins of rank differentiation and social hierarchy in human societies. Conflict models suggest that the formation of social hierarchies is synonymous with the establishment of relationships of coercive social dominance and exploitation. Voluntary or 'integrative' models, on the other hand, suggest that rank differentiation--the differentiation of leader from follower, ruler from ruled, or state from subject--may sometimes be preferred over more egalitarian social arrangements as a solution to the challenges of life in social groups, such as conflict over resources, coordination failures, and free-riding in cooperative relationships. Little formal theoretical work, however, has established whether and under what conditions individuals would indeed prefer the establishment of more hierarchical relationships over more egalitarian alternatives. This paper provides an evolutionary game theoretical model for the acceptance of leadership in cooperative groups. We propose that the effort of a leader can reduce the likelihood that cooperation fails due to free-riding or coordination errors, and that under some circumstances, individuals would prefer to cooperate in a group under the supervision of a leader who receives a share of the group's productivity than to work in an unsupervised group. We suggest, in particular, that this becomes an optimal solution for individual decision makers when the number of group members required for collective action exceeds the maximum group size at which leaderless cooperation is viable.
Chaos and order in non-integrable model field theories
Campbell, D.K.; Peyrard, M.
1989-01-01
We illustrate the presence of chaos and order in non-integrable, classical field theories, which we view as many-degree-of-freedom Hamiltonian nonlinear dynamical systems. For definiteness, we focus on the {chi}{sup 4} theory and compare and contrast it with the celebrated integrable sine-Gordon equation. We introduce and investigate two specific problems: the interactions of solitary kink''-like waves in non-integrable theories; and the existence of stable breather'' solutions -- spatially-localized, time-periodic nonlinear waves -- in the {chi}{sup 4} theory. For the former problem we review the rather well developed understanding, based on a combination of computational simulations and heuristic analytic models, of the presence of a sequence of resonances in the kink-antikink interactions as a function of the relative velocity of the interaction. For the latter problem we discuss first the case of the continuum {chi}{sup 4} theory. We discuss the multiple-scale asymptotic perturbation theory arguments which first suggested the existence of {chi}{sup 4} breathers, then the subsequent discovery of terms beyond-all-orders'' in the perturbation expansion which destroy the putative breather, and finally, the recent rigorous proofs of the non-existence of breathers in the continuum theory. We then present some very recent numerical results on the existence of breathers in discrete {chi}{sup 4} theories which show an intricate interweaving of stable and unstable breather solutions on finite discrete lattices. We develop a heuristic theoretical explanation of the regions of stability and instability.
Precision Higgs Physics, Effective Field Theory, and Dark Matter
NASA Astrophysics Data System (ADS)
Henning, Brian Quinn
The recent discovery of the Higgs boson calls for detailed studies of its properties. As precision measurements are indirect probes of new physics, the appropriate theoretical framework is effective field theory. In the first part of this thesis, we present a practical three-step procedure of using the Standard Model effective field theory (SM EFT) to connect ultraviolet (UV) models of new physics with weak scale precision observables. With this procedure, one can interpret precision measurements as constraints on the UV model concerned. We give a detailed explanation for calculating the effective action up to one-loop order in a manifestly gauge covariant fashion. The covariant derivative expansion dramatically simplifies the process of matching a UV model with the SM EFT, and also makes available a universal formalism that is easy to use for a variety of UV models. A few general aspects of renormalization group running effects and choosing operator bases are discussed. Finally, we provide mapping results between the bosonic sector of the SM EFT and a complete set of precision electroweak and Higgs observables to which present and near future experiments are sensitive. With a detailed understanding of how to use the SM EFT, we then turn to applications and study in detail two well-motivated test cases. The first is singlet scalar field that enables the first-order electroweak phase transition for baryogenesis; the second example is due to scalar tops in the MSSM. We find both Higgs and electroweak measurements are sensitive probes of these cases. The second part of this thesis centers around dark matter, and consists of two studies. In the first, we examine the effects of relic dark matter annihilations on big bang nucleosynthesis (BBN). The magnitude of these effects scale simply with the dark matter mass and annihilation cross-section, which we derive. Estimates based on these scaling behaviors indicate that BBN severely constrains hadronic and radiative dark
Group Motivation and Group Task Performance: The Expectancy-Valence Theory Approach.
ERIC Educational Resources Information Center
Nakanishi, Masayuki
1988-01-01
Investigated effects of group motivation on group task performance. Created two levels of valence, expectancy and instrumentality. Valence variable reflected on group productivity on unstructured and task persistence measures. Expectancy variable's effect was on task persistence measure. Instrumentality affected group productivity on structured…
From effective field theories to effective density functionals in and beyond the mean field
NASA Astrophysics Data System (ADS)
Grasso, M.; Lacroix, D.; van Kolck, U.
2016-06-01
Since the 1975 Nobel Prize in Physics, nuclear theory has evolved along two main directions. On the one hand, the energy-density functional (EDF) theory was established, which presently encompasses (by enlarging the EDF framework) all the mean-field and beyond-mean-field theories based on energy functionals produced by effective phenomenological interactions. Highly sophisticated structure and reaction models are currently available for the treatment of medium-mass and heavy nuclei. On the other hand, effective field theories (EFTs) have rendered possible the formulation of QCD as a low-energy hadronic theory. Ab initio methods have recently achieved remarkable success in the application of EFT or EFT-inspired potentials to structure analyses of light nuclei. Different but complementary competences have been developed during the past few decades in the EDF and EFT communities. Bridges and connections have in some cases been identified and constructed. We review here some of the developments that have been performed within the EDF theory and the EFT during recent years, with some emphasis on analogies and connections that may one day provide a unified picture of the two theories. Illustrations are given for infinite matter and finite nuclei.
From effective field theories to effective density functionals in and beyond the mean field
NASA Astrophysics Data System (ADS)
Grasso, M.; Lacroix, D.; van Kolck, U.
2016-06-01
Since the 1975 Nobel Prize in Physics, nuclear theory has evolved along two main directions. On the one hand, the energy–density functional (EDF) theory was established, which presently encompasses (by enlarging the EDF framework) all the mean-field and beyond-mean-field theories based on energy functionals produced by effective phenomenological interactions. Highly sophisticated structure and reaction models are currently available for the treatment of medium-mass and heavy nuclei. On the other hand, effective field theories (EFTs) have rendered possible the formulation of QCD as a low-energy hadronic theory. Ab initio methods have recently achieved remarkable success in the application of EFT or EFT-inspired potentials to structure analyses of light nuclei. Different but complementary competences have been developed during the past few decades in the EDF and EFT communities. Bridges and connections have in some cases been identified and constructed. We review here some of the developments that have been performed within the EDF theory and the EFT during recent years, with some emphasis on analogies and connections that may one day provide a unified picture of the two theories. Illustrations are given for infinite matter and finite nuclei.
Discrete field theories and spatial properties of strings
Klebanov, I.; Susskind, L.
1988-10-01
We use the ground-state wave function in the light-cone gauge to study the spatial properties of fundamental strings. We find that, as the cut-off in the parameter space is removed, the strings are smooth and have a divergent size. Guided by these properties, we consider a large-N lattice gauge theory which has an unstable phase where the size of strings diverges. We show that this phase exactly describes free fundamental strings. The lattice spacing does not have to be taken to zero for this equivalence to hold. Thus, exact rotation and translation invariance is restored in a discrete space. This suggests that the number of fundamental short-distance degrees of freedom in string theory is much smaller than in a conventional field theory. 11 refs., 4 figs.
Analysis of general power counting rules in effective field theory
NASA Astrophysics Data System (ADS)
Gavela, Belen; Jenkins, Elizabeth E.; Manohar, Aneesh V.; Merlo, Luca
2016-09-01
We derive the general counting rules for a quantum effective field theory (EFT) in {d} dimensions. The rules are valid for strongly and weakly coupled theories, and they predict that all kinetic energy terms are canonically normalized. They determine the energy dependence of scattering cross sections in the range of validity of the EFT expansion. We show that the size of the cross sections is controlled by the Λ power counting of EFT, not by chiral counting, even for chiral perturbation theory (χ PT). The relation between Λ and f is generalized to {d} dimensions. We show that the naive dimensional analysis 4π counting is related to hbar counting. The EFT counting rules are applied to χ PT, low-energy weak interactions, Standard Model EFT and the non-trivial case of Higgs EFT.
Cluster-like coordinates in supersymmetric quantum field theory
Neitzke, Andrew
2014-01-01
Recently it has become apparent that N=2 supersymmetric quantum field theory has something to do with cluster algebras. I review one aspect of the connection: supersymmetric quantum field theories have associated hyperkähler moduli spaces, and these moduli spaces carry a structure that looks like an extension of the notion of cluster variety. In particular, one encounters the usual variables and mutations of the cluster story, along with more exotic extra variables and generalized mutations. I focus on a class of examples where the underlying cluster varieties are moduli spaces of flat connections on surfaces, as considered by Fock and Goncharov [Fock V, Goncharov A (2006) Publ Math Inst Hautes Études Sci 103:1–211]. The work reviewed here is largely joint with Davide Gaiotto and Greg Moore. PMID:24982190
Tachyon solutions in boundary and open string field theory
Calcagni, Gianluca; Nardelli, Giuseppe
2008-12-15
We construct rolling tachyon solutions of open and boundary string field theory (OSFT and BSFT, respectively), in the bosonic and supersymmetric (susy) case. The wildly oscillating solution of susy OSFT is recovered, together with a family of time-dependent BSFT solutions, for the bosonic and susy string. These are parametrized by an arbitrary constant r involved in solving the Green equation of the target fields. When r=0 we recover previous results in BSFT, whereas for r attaining the value predicted by OSFT it is shown that the bosonic OSFT solution is the derivative of the boundary one; in the supersymmetric case the relation between the two solutions is more complicated. This technical correspondence sheds some light on the nature of wild oscillations, which appear in both theories whenever r>0.
The adhesion model as a field theory for cosmological clustering
Rigopoulos, Gerasimos
2015-01-01
The adhesion model has been proposed in the past as an improvement of the Zel'dovich approximation, providing a good description of the formation of the cosmic web. We recast the model as a field theory for cosmological large scale structure, adding a stochastic force to account for power generated from very short, highly non-linear scales that is uncorrelated with the initial power spectrum. The dynamics of this Stochastic Adhesion Model (SAM) is reminiscent of the well known Kardar-Parisi-Zhang equation with the difference that the viscosity and the noise spectrum are time dependent. Choosing the viscosity proportional to the growth factor D restricts the form of noise spectrum through a 1-loop renormalization argument. For this choice, the SAM field theory is renormalizable to one loop. We comment on the suitability of this model for describing the non-linear regime of the CDM power spectrum and its utility as a relatively simple approach to cosmological clustering.
Locally smeared operator product expansions in scalar field theory
Monahan, Christopher; Orginos, Kostas
2015-04-01
We propose a new locally smeared operator product expansion to decompose non-local operators in terms of a basis of smeared operators. The smeared operator product expansion formally connects nonperturbative matrix elements determined numerically using lattice field theory to matrix elements of non-local operators in the continuum. These nonperturbative matrix elements do not suffer from power-divergent mixing on the lattice, which significantly complicates calculations of quantities such as the moments of parton distribution functions, provided the smearing scale is kept fixed in the continuum limit. The presence of this smearing scale complicates the connection to the Wilson coefficients of the standardmore » operator product expansion and requires the construction of a suitable formalism. We demonstrate the feasibility of our approach with examples in real scalar field theory.« less
Cluster-like coordinates in supersymmetric quantum field theory.
Neitzke, Andrew
2014-07-01
Recently it has become apparent that N = 2 supersymmetric quantum field theory has something to do with cluster algebras. I review one aspect of the connection: supersymmetric quantum field theories have associated hyperkähler moduli spaces, and these moduli spaces carry a structure that looks like an extension of the notion of cluster variety. In particular, one encounters the usual variables and mutations of the cluster story, along with more exotic extra variables and generalized mutations. I focus on a class of examples where the underlying cluster varieties are moduli spaces of flat connections on surfaces, as considered by Fock and Goncharov [Fock V, Goncharov A (2006) Publ Math Inst Hautes Études Sci 103:1-211]. The work reviewed here is largely joint with Davide Gaiotto and Greg Moore.
Locally smeared operator product expansions in scalar field theory
Monahan, Christopher; Orginos, Kostas
2015-04-01
We propose a new locally smeared operator product expansion to decompose non-local operators in terms of a basis of smeared operators. The smeared operator product expansion formally connects nonperturbative matrix elements determined numerically using lattice field theory to matrix elements of non-local operators in the continuum. These nonperturbative matrix elements do not suffer from power-divergent mixing on the lattice, which significantly complicates calculations of quantities such as the moments of parton distribution functions, provided the smearing scale is kept fixed in the continuum limit. The presence of this smearing scale complicates the connection to the Wilson coefficients of the standard operator product expansion and requires the construction of a suitable formalism. We demonstrate the feasibility of our approach with examples in real scalar field theory.
Rom, Eldad; Mikulincer, Mario
2003-06-01
Four studies examined attachment-style differences in group-related cognitions and behaviors. In Studies 1-2, participants completed scales on group-related cognitions and emotions. In Studies 3-4, participants were divided into small groups, and their performance in group tasks as well as the cohesion of their group were assessed. Both attachment anxiety and avoidance in close relationships were associated with negative group-related cognitions and emotions. Anxiety was also related to the pursuit of closeness goals and impaired instrumental performance in group tasks. Avoidance was related to the pursuit of distance goals and deficits in socioemotional and instrumental performance. Group cohesion significantly moderated the effects of attachment anxiety. The discussion emphasizes the relevance of attachment theory within group contexts. PMID:12793586
Rom, Eldad; Mikulincer, Mario
2003-06-01
Four studies examined attachment-style differences in group-related cognitions and behaviors. In Studies 1-2, participants completed scales on group-related cognitions and emotions. In Studies 3-4, participants were divided into small groups, and their performance in group tasks as well as the cohesion of their group were assessed. Both attachment anxiety and avoidance in close relationships were associated with negative group-related cognitions and emotions. Anxiety was also related to the pursuit of closeness goals and impaired instrumental performance in group tasks. Avoidance was related to the pursuit of distance goals and deficits in socioemotional and instrumental performance. Group cohesion significantly moderated the effects of attachment anxiety. The discussion emphasizes the relevance of attachment theory within group contexts.
E8(8) exceptional field theory: geometry, fermions and supersymmetry
NASA Astrophysics Data System (ADS)
Baguet, Arnaud; Samtleben, Henning
2016-09-01
We present the supersymmetric extension of the recently constructed E8(8) exceptional field theory — the manifestly U-duality covariant formulation of the untruncated ten- and eleven-dimensional supergravities. This theory is formulated on a (3+248) dimensional spacetime (modulo section constraint) in which the extended coordinates transform in the adjoint representation of E8(8). All bosonic fields are E8(8) tensors and transform under internal generalized diffeomorphisms. The fermions are tensors under the generalized Lorentz group SO(1, 2) × SO(16), where SO(16) is the maximal compact subgroup of E8(8). Vanishing generalized torsion determines the corresponding spin connections to the extent they are required to formulate the field equations and supersymmetry transformation laws. We determine the supersymmetry transformations for all bosonic and fermionic fields such that they consistently close into generalized diffeomorphisms. In particular, the covariantly constrained gauge vectors of E8(8) exceptional field theory combine with the standard supergravity fields into a single supermultiplet. We give the complete extended Lagrangian and show its invariance under supersymmetry. Upon solution of the section constraint the theory reduces to full D=11 or type IIB supergravity.
The Interaction of Field Theory, Family Systems Theory, and Children's Rights.
ERIC Educational Resources Information Center
Schwartz, Lita Linzer
1993-01-01
Field theory is interactional. It asserts that genetic predispositions, acquired characteristics, uniqueness, and behaviors of individual impact are affected by events and people in environment. This can be seen clearly in development of children who join family rather than being born into it. Resulting complexities can be seen in family therapy…
An Assessment of Evans' Unified Field Theory I
NASA Astrophysics Data System (ADS)
Hehl, Friedrich W.
2008-01-01
Evans developed a classical unified field theory of gravitation and electromagnetism on the background of a spacetime obeying a Riemann-Cartan geometry. This geometry can be characterized by an orthonormal coframe ϑ α and a (metric compatible) Lorentz connection Γ α β . These two potentials yield the field strengths torsion T α and curvature R α β . Evans tried to infuse electromagnetic properties into this geometrical framework by putting the coframe ϑ α to be proportional to four extended electromagnetic potentials mathcal{A}^{α } ; these are assumed to encompass the conventional Maxwellian potential A in a suitable limit. The viable Einstein-Cartan (-Sciama-Kibble) theory of gravity was adopted by Evans to describe the gravitational sector of his theory. Including also the results of an accompanying paper by Obukhov and the author, we show that Evans’ ansatz for electromagnetism is untenable beyond repair both from a geometrical as well as from a physical point of view. As a consequence, his unified theory is obsolete.
Vakonomic Constraints in Higher-Order Classical Field Theory
NASA Astrophysics Data System (ADS)
Campos, Cédric M.
2010-07-01
We propose a differential-geometric setting for the dynamics of a higher-order field theory, based on the Skinner and Rusk formalism for mechanics. This approach incorporates aspects of both, the Lagrangian and the Hamiltonian description, since the field equations are formulated using the Lagrangian on a higher-order jet bundle and the canonical multisymplectic form on its affine dual. The result is that we obtain a unique and global intrinsic description of the dynamics. The case of vakonomic constraints is also studied within this formalism.
Multisymplectic Lagrangian and Hamiltonian Formalisms of Classical Field Theories
NASA Astrophysics Data System (ADS)
Román-Roy, Narciso
2009-11-01
This review paper is devoted to presenting the standard multisymplectic formulation for describing geometrically classical field theories, both the regular and singular cases. First, the main features of the Lagrangian formalism are revisited and, second, the Hamiltonian formalism is constructed using Hamiltonian sections. In both cases, the variational principles leading to the Euler-Lagrange and the Hamilton-De Donder-Weyl equations, respectively, are stated, and these field equations are given in different but equivalent geometrical ways in each formalism. Finally, both are unified in a new formulation (which has been developed in the last years), following the original ideas of Rusk and Skinner for mechanical systems.
Quantum κ-deformed differential geometry and field theory
NASA Astrophysics Data System (ADS)
Mercati, Flavio
2016-03-01
I introduce in κ-Minkowski noncommutative spacetime the basic tools of quantum differential geometry, namely bicovariant differential calculus, Lie and inner derivatives, the integral, the Hodge-∗ and the metric. I show the relevance of these tools for field theory with an application to complex scalar field, for which I am able to identify a vector-valued four-form which generalizes the energy-momentum tensor. Its closedness is proved, expressing in a covariant form the conservation of energy-momentum.
Conformal field theory of critical Casimir interactions in 2D
NASA Astrophysics Data System (ADS)
Bimonte, G.; Emig, T.; Kardar, M.
2013-10-01
Thermal fluctuations of a critical system induce long-ranged Casimir forces between objects that couple to the underlying field. For two-dimensional (2D) conformal field theories (CFT) we derive an exact result for the Casimir interaction between two objects of arbitrary shape, in terms of 1) the free energy of a circular ring whose radii are determined by the mutual capacitance of two conductors with the objects' shape; and 2) a purely geometric energy that is proportional to the conformal charge of the CFT, but otherwise super-universal in that it depends only on the shapes and is independent of boundary conditions and other details.
Causal field theory with an infinite speed of sound
Afshordi, Niayesh; Chung, Daniel J. H.; Geshnizjani, Ghazal
2007-04-15
We introduce a model of scalar field dark energy, Cuscuton, which can be realized as the incompressible (or infinite speed of sound) limit of a scalar field theory with a noncanonical kinetic term (or k-essence). Even though perturbations of Cuscuton propagate superluminally, we show that they have a locally degenerate phase space volume (or zero entropy), implying that they cannot carry any microscopic information, and thus the theory is causal. Even coupling to ordinary scalar fields cannot lead to superluminal signal propagation. Furthermore, we show that the family of constant field hypersurfaces is the family of constant mean curvature hypersurfaces, which are the analogs of soap films (or soap bubbles) in Euclidian space. This enables us to find the most general solution in 1+1 dimensions, whose properties motivate conjectures for global degeneracy of the phase space in higher dimensions. Finally, we show that the Cuscuton action can model the continuum limit of the evolution of a field with discrete degrees of freedom and argue why it is protected against quantum corrections at low energies. While this paper mainly focuses on interesting features of Cuscuton in a Minkowski space-time, a companion paper examines cosmology with Cuscuton dark energy.
Approach to non-equilibrium behaviour in quantum field theory
Kripfganz, J.; Perlt, H.
1989-05-01
We study the real-time evolution of quantum field theoretic systems in non-equilibrium situations. Results are presented for the example of scalar /lambda//phi//sup 4/ theory. The degrees of freedom are discretized by studying the system on a torus. Short-wavelength modes are integrated out to one-loop order. The long-wavelength modes considered to be the relevant degrees of freedom are treated by semiclassical phase-space methods. /copyright/ 1989 Academic Press, Inc.
Generating functionals for Green's functions in gauge field theories
Bordag, M.; Kaschlun, L.; Matveev, V.A.; Robaschik, D.
1987-09-01
The structure of the generating functional of the one-particle-irreducible Green's functions in gauge field theories is investigated. Both axial as well as covariant gauge conditions are considered. For both cases, the general structure of the functionals is obtained, and a functional expansion with respect to nonlocal operators is given. The appearance of gauge-dependent operators in the case of the covariant gauge follows in a natural manner from the structure of the corresponding functional.
Quantum electrodynamics in finite volume and nonrelativistic effective field theories
NASA Astrophysics Data System (ADS)
Fodor, Z.; Hoelbling, C.; Katz, S. D.; Lellouch, L.; Portelli, A.; Szabo, K. K.; Toth, B. C.
2016-04-01
Electromagnetic effects are increasingly being accounted for in lattice quantum chromodynamics computations. Because of their long-range nature, they lead to large finite-size effects over which it is important to gain analytical control. Nonrelativistic effective field theories provide an efficient tool to describe these effects. Here we argue that some care has to be taken when applying these methods to quantum electrodynamics in a finite volume.
Four-nucleon force in chiral effective field theory
Evgeny Epelbaum
2005-10-25
We derive the leading contribution to the four--nucleon force within the framework of chiral effective field theory. It is governed by the exchange of pions and the lowest--order nucleon--nucleon contact interaction and includes effects due to the nonlinear pion--nucleon couplings and the pion self interactions constrained by the chiral symmetry of QCD. The resulting 4NF does not contain any unknown parameters and can be tested in future few--and many--nucleon studies.
Horava—Lifshitz Type Quantum Field Theory and Hierarchy Problem
NASA Astrophysics Data System (ADS)
Wei, Chao
2016-06-01
We study the Lifshitz type extension of the standard model (SM) at the UV, with dynamical critical exponent z = 3. One loop radiative corrections to the Higgs mass in such a model are calculated. Our result shows that, the Hierarchy problem, which has initiated many excellent extension of the minimal SM, may be weakened in the z = 3 Lifshitz type quantum field theory. Supported by the National Natural Science Foundation of China
Schwinger-Dyson approach to Liouville field theory
NASA Astrophysics Data System (ADS)
Dutta, P.
2016-06-01
We discuss Liouville field theory in the framework of the Schwinger-Dyson approach and derive a functional equation for the three-point structure constant. We prove the existence of a second Schwinger-Dyson equation based on the duality between the screening charge operators and obtain a second functional equation for the structure constant. We use the system of these two equations to uniquely determine the structure constant.
Bogoliubov transformations and fermion condensates in lattice field theories
Caracciolo, Sergio Palumbo, Fabrizio Viola, Giovanni
2009-03-15
We apply generalized Bogoliubov transformations to the transfer matrix of relativistic field theories regularized on a lattice. We derive the conditions these transformations must satisfy to factorize the transfer matrix into two terms which propagate fermions and antifermions separately, and we solve the relative equations under some conditions. We relate these equations to the saddle point approximation of a recent bosonization method and to the Foldy-Wouthuysen transformations which separate positive from negative energy states in the Dirac Hamiltonian.
Betelgeusean Physics: A Possible Ansatz to a Unified Field Theory
NASA Astrophysics Data System (ADS)
Lorenz Vrba, Anton
I use spherical-numbers to model and study interacting wave functions, and recover known physical laws. A wavefunction interacts with and changes space; the natural forces and quantum properties emerge. The study describes an absolute reality that withstands the tests of relativity. A Bohr-like model of the hydrogen atom dilates the transition frequencies. This alternate approach could provide an ansatz for a unified field theory, however it has a price; most present-day accepted truths need revision.
Three-Body Nuclear Systems in Pionless Effective Field Theory
NASA Astrophysics Data System (ADS)
Vanasse, Jared
2016-03-01
New perturbative techniques for three-body systems with contact interactions are discussed. Their application to pionless effective field theory (EF{Tnot π }) for nd scattering is shown, and their extension to bound states addressed. With the extension to bound states a leading-order EF{Tnot π } calculation of the triton charge radius and novel treatments of three-body forces are discussed.
American Pluralism: A Study of Minority Groups and Social Theory.
ERIC Educational Resources Information Center
Newman, William M.
This book addresses some basic issues and topics in the sociology of majority-minority relationships and attempts to evaluate and reformulate the conceptual and theoretical tools of the field. It is argued in Part I that majority-minority relationships must be understood as a case study in social stratification and as an opportunity for the study…
A study of the current group evaporation/combustion theories
NASA Technical Reports Server (NTRS)
Shen, Hayley H.
1990-01-01
Liquid fuel combustion can be greatly enhanced by disintegrating the liquid fuel into droplets, an effect achieved by various configurations. A number of experiments carried out in the seventies showed that combustion of droplet arrays and sprays do not form individual flames. Moreover, the rate of burning in spray combustion greatly deviates from that of the single combustion rate. Such observations naturally challenge its applicability to spray combustion. A number of mathematical models were developed to evaluate 'group combustion' and the related 'group evaporation' phenomena. This study investigates the similarity and difference of these models and their applicability to spray combustion. Future work that should be carried out in this area is indicated.
NASA Astrophysics Data System (ADS)
Bibak, Khodakhast; Kapron, Bruce M.; Srinivasan, Venkatesh
2016-09-01
Graphs embedded into surfaces have many important applications, in particular, in combinatorics, geometry, and physics. For example, ribbon graphs and their counting is of great interest in string theory and quantum field theory (QFT). Recently, Koch et al. (2013) [12] gave a refined formula for counting ribbon graphs and discussed its applications to several physics problems. An important factor in this formula is the number of surface-kernel epimorphisms from a co-compact Fuchsian group to a cyclic group. The aim of this paper is to give an explicit and practical formula for the number of such epimorphisms. As a consequence, we obtain an 'equivalent' form of Harvey's famous theorem on the cyclic groups of automorphisms of compact Riemann surfaces. Our main tool is an explicit formula for the number of solutions of restricted linear congruence recently proved by Bibak et al. using properties of Ramanujan sums and of the finite Fourier transform of arithmetic functions.
Locality of Gravitational Systems from Entanglement of Conformal Field Theories.
Lin, Jennifer; Marcolli, Matilde; Ooguri, Hirosi; Stoica, Bogdan
2015-06-01
The Ryu-Takayanagi formula relates the entanglement entropy in a conformal field theory to the area of a minimal surface in its holographic dual. We show that this relation can be inverted for any state in the conformal field theory to compute the bulk stress-energy tensor near the boundary of the bulk spacetime, reconstructing the local data in the bulk from the entanglement on the boundary. We also show that positivity, monotonicity, and convexity of the relative entropy for small spherical domains between the reduced density matrices of any state and of the ground state of the conformal field theory are guaranteed by positivity conditions on the bulk matter energy density. As positivity and monotonicity of the relative entropy are general properties of quantum systems, this can be interpreted as a derivation of bulk energy conditions in any holographic system for which the Ryu-Takayanagi prescription applies. We discuss an information theoretical interpretation of the convexity in terms of the Fisher metric.
Dynamical mean-field theory for flat-band ferromagnetism
NASA Astrophysics Data System (ADS)
Nguyen, Hong-Son; Tran, Minh-Tien
2016-09-01
The magnetically ordered phase in the Hubbard model on the infinite-dimensional hyper-perovskite lattice is investigated within dynamical mean-field theory. It turns out for the infinite-dimensional hyper-perovskite lattice the self-consistent equations of dynamical mean-field theory are exactly solved, and this makes the Hubbard model exactly solvable. We find electron spins are aligned in the ferromagnetic or ferrimagnetic configuration at zero temperature and half filling of the edge-centered sites of the hyper-perovskite lattice. A ferromagnetic-ferrimagnetic phase transition driven by the energy level splitting is found and it occurs through a phase separation. The origin of ferromagnetism and ferrimagnetism arises from the band flatness and the virtual hybridization between macroscopically degenerate flat bands and dispersive ones. Based on the exact solution in the infinite-dimensional limit, a modified exact diagonalization as the impurity solver for dynamical mean-field theory on finite-dimensional perovskite lattices is also proposed and examined.
Hamiltonian truncation approach to quenches in the Ising field theory
NASA Astrophysics Data System (ADS)
Rakovszky, T.; Mestyán, M.; Collura, M.; Kormos, M.; Takács, G.
2016-10-01
In contrast to lattice systems where powerful numerical techniques such as matrix product state based methods are available to study the non-equilibrium dynamics, the non-equilibrium behaviour of continuum systems is much harder to simulate. We demonstrate here that Hamiltonian truncation methods can be efficiently applied to this problem, by studying the quantum quench dynamics of the 1 + 1 dimensional Ising field theory using a truncated free fermionic space approach. After benchmarking the method with integrable quenches corresponding to changing the mass in a free Majorana fermion field theory, we study the effect of an integrability breaking perturbation by the longitudinal magnetic field. In both the ferromagnetic and paramagnetic phases of the model we find persistent oscillations with frequencies set by the low-lying particle excitations not only for small, but even for moderate size quenches. In the ferromagnetic phase these particles are the various non-perturbative confined bound states of the domain wall excitations, while in the paramagnetic phase the single magnon excitation governs the dynamics, allowing us to capture the time evolution of the magnetisation using a combination of known results from perturbation theory and form factor based methods. We point out that the dominance of low lying excitations allows for the numerical or experimental determination of the mass spectra through the study of the quench dynamics.
Relativistic gravity and parity-violating nonrelativistic effective field theories
NASA Astrophysics Data System (ADS)
Wu, Chaolun; Wu, Shao-Feng
2015-06-01
We show that the relativistic gravity theory can offer a framework to formulate the nonrelativistic effective field theory in a general coordinate invariant way. We focus on the parity violating case in 2 +1 dimensions which is particularly appropriate for the study on quantum Hall effects and chiral superfluids. We discuss how the nonrelativistic spacetime structure emerges from relativistic gravity. We present covariant maps and constraints that relate the field contents in the two theories, which also serve as the holographic dictionary in the context of gauge/gravity duality. A low energy effective action for fractional quantum Hall states is constructed, which captures universal geometric properties and generates nonuniversal corrections systematically. We give another holographic example with dyonic black brane background to calculate thermodynamic and transport properties of strongly coupled nonrelativistic fluids in magnetic field. In particular, by identifying the shift function in the gravity as a minus of guiding center velocity, we obtain the Hall viscosity with its relation to Landau orbital angular momentum density proportional to Wen-Zee shift. Our formalism has a good projection to lowest Landau level.
Axionic field theory of (3+1)-dimensional Weyl semimetals
NASA Astrophysics Data System (ADS)
Goswami, Pallab; Tewari, Sumanta
2013-12-01
From a direct calculation of the anomalous Hall conductivity and an effective electromagnetic action obtained via Fujikawa's chiral rotation technique, we conclude that an axionic field theory with a nonquantized coefficient describes the electromagnetic response of the (3+1)-dimensional Weyl semimetal. The coefficient is proportional to the momentum space separation of the Weyl nodes. Akin to the Chern-Simons field theory of quantum Hall effect, the axion field theory violates gauge invariance in the presence of the boundary, which is cured by the chiral anomaly of the surface states via the Callan-Harvey mechanism. This provides a unique solution for the radiatively induced CPT-odd term in the electromagnetic polarization tensor of the Lorentz violating spinor electrodynamics, where the source of the Lorentz violation is a constant axial 4-vector term for the Dirac fermion. A direct linear response calculation also establishes anomalous thermal Hall effect and a Wiedemann-Franz law, but thermal Hall conductivity does not directly follow from the well known formula for the gravitational chiral anomaly.
Gauge transformation of double field theory for open string
NASA Astrophysics Data System (ADS)
Ma, Chen-Te
2015-09-01
We combine symmetry structures of ordinary (parallel directions) and dual (transversal directions) coordinates to construct the Dirac-Born-Infeld theory. The ordinary coordinates are associated with the Neumann boundary conditions and the dual coordinates are associated with the Dirichlet boundary conditions. Gauge fields become scalar fields by exchanging the ordinary and dual coordinates. A gauge transformation of a generalized metric is governed by the generalized Lie derivative. The gauge transformation of the massless closed string theory gives the C -bracket, but the gauge transformation of the open string theory gives the F -bracket. The F -bracket with the strong constraints is different from the Courant bracket by an exact one-form. This exact one-form should come from the one-form gauge field. Based on a symmetry point of view, we deduce a suitable action with a nonzero H -flux at the low-energy level. From an equation of motion of the scalar dilaton, it defines a generalized scalar curvature. Finally, we construct a double sigma model with a boundary term and show that this model with constraints is classically equivalent to the ordinary sigma model.
Effective field theory for massive gravitons and gravity in theory space
NASA Astrophysics Data System (ADS)
Arkani-Hamed, Nima; Georgi, Howard; Schwartz, Matthew D.
2003-06-01
We introduce a technique for restoring general coordinate invariance into theories where it is explicitly broken. This is the analog for gravity of the Callan-Coleman-Wess-Zumino formalism for gauge theories. We use this to elucidate the properties of interacting massless and massive gravitons. For a single graviton with a Planck scale MPl and a mass mg, we find that there is a sensible effective field theory which is valid up to a high-energy cutoff Λ parametrically above mg. Our methods allow for a transparent understanding of the many peculiarities associated with massive gravitons, among them the need for the Fierz-Pauli form of the Lagrangian, the presence or absence of the van Dam-Veltman-Zakharov discontinuity in general backgrounds, and the onset of non-linear effects and the breakdown of the effective theory at large distances from heavy sources. The natural sizes of all non-linear corrections beyond the Fierz-Pauli term are easily determined. The cutoff scales as Λ˜( mg4MPl) 1/5 for the Fierz-Pauli theory, but can be raised to Λ˜( mg2MPl) 1/3 in certain non-linear extensions. Having established that these models make sense as effective theories, there are a number of new avenues for exploration, including model building with gravity in theory space and constructing gravitational dimensions.
Quantum Chromodynamics -- The Perfect Yang-Mills Gauge Field Theory
NASA Astrophysics Data System (ADS)
Gross, David
David Gross: My talk today is about the most beautiful of all Yang-Mills Theories (non-Abelian gauge theories), the theory of the strong nuclear interactions, Quantum Chromodynamics, QCD. We are celebrating 60 years of the publication of a remarkable paper which introduced the concept of non-Abelian local gauge symmetries, now called the Yang-Mills theory, to physics. In the introduction to this paper it is noted that the usual principle of isotopic spin symmetry is not consistent with the concept of localized fields. This sentence has drawn attention over the years because the usual principle of isotopic spin symmetry is consistent, it is just not satisfactory. The authors, Yang and Mills, introduced a more satisfactory notion of local symmetry which did not require one to rotate (in isotopic spin space) the whole universe at once to achieve the symmetry transformation. Global symmetries are thus are similar to `action at a distance', whereas Yang-Mills theory is manifestly local...
Dual of the Janus solution: An interface conformal field theory
NASA Astrophysics Data System (ADS)
Clark, A. B.; Freedman, D. Z.; Karch, A.; Schnabl, M.
2005-03-01
We propose and study a specific gauge theory dual of the smooth, nonsupersymmetric (and apparently stable) Janus solution of Type IIB supergravity found in Bak et al. [J. High Energy Phys., JHEPFG, 1029-8479 05 (2003) 072]. The dual field theory is N=4 SYM theory on two half-spaces separated by a planar interface with different coupling constants in each half-space. We assume that the position dependent coupling multiplies the operator L' which is the fourth descendent of the primary TrX{IXJ} and closely related to the N=4 Lagrangian density. At the classical level supersymmetry is broken explicitly, but SO(3,2) conformal symmetry is preserved. We use conformal perturbation theory to study various correlation functions to first and second order in the discontinuity of g2YM, confirming quantum level conformal symmetry. Certain quantities such as the vacuum expectation value
Fuentes, Agustin; Kissel, Marc
2016-01-01
Richerson et al. provide a much needed roadmap for assessing cultural group selection (CGS) theory and for applying it to understanding variation between contemporary human groups. However, the current proposal lacks connection to relevant evidence from the human evolutionary record and requires a better integration with contemporary evolutionary theory. The article also misapplies the F st statistic. PMID:27562510
ERIC Educational Resources Information Center
Wang, Lihua
2012-01-01
A new method is introduced for teaching group theory analysis of the infrared spectra of organometallic compounds using molecular modeling. The main focus of this method is to enhance student understanding of the symmetry properties of vibrational modes and of the group theory analysis of infrared (IR) spectra by using visual aids provided by…
School Finance and Technology: A Case Study Using Grid and Group Theory to Explore the Connections
ERIC Educational Resources Information Center
Case, Stephoni; Harris, Edward L.
2014-01-01
Using grid and group theory (Douglas 1982, 2011), the study described in this article examined the intersections of technology and school finance in four schools located in districts differing in size, wealth, and commitment to technology integration. In grid and group theory, grid refers to the degree to which policies and role prescriptions…
Group Learning Assessment: Developing a Theory-Informed Analytics
ERIC Educational Resources Information Center
Xing, Wanli; Wadholm, Robert; Petakovic, Eva; Goggins, Sean
2015-01-01
Assessment in Computer Supported Collaborative Learning (CSCL) is an implicit issue, and most assessments are summative in nature. Process-oriented methods of assessment can vary significantly in their indicators and typically only partially address the complexity of group learning. Moreover, the majority of these assessment methods require…
The Large-N Limit of Superconformal Field Theories and Supergravity
NASA Astrophysics Data System (ADS)
Maldacena, Juan
We show that the large-N limits of certainconformal field theories in various dimensions includein their Hilbert space a sector describing supergravityon the product of anti-de Sitter spacetimes, spheres, and other compact manifolds. This is shown bytaking some branes in the full M/string theory and thentaking a low-energy limit where the field theory on thebrane decouples from the bulk. We observe that, in this limit, we can still trust thenear-horizon geometry for large N. The enhancedsupersymmetries of the near-horizon geometry correspondto the extra supersymmetry generators present in thesuperconformal group (as opposed to just the super-Poincaregroup). The 't Hooft limit of 3 + 1 N = 4 super-Yang?Mills at the conformal pointis shown to contain strings: they are IIB strings. Weconjecture that compactifications of M/string theory on various anti-de Sitterspacetimes is dual to various conformal field theories.This leads to a new proposal for a definition ofM-theory which could be extended to include fivenoncompact dimensions.
Gauge Invariant U(1) Field Theories with Magnetic Monopole Symmetry.
NASA Astrophysics Data System (ADS)
Goldman, Neil
1982-03-01
A quantum field theory of a magnetically and electrically charged fermion field is developed. This is done for an abelian duet of vector boson fields in a U(1), gauge invariant manner. The U(1) symmetry is maintained through a scalar field interacting with the boson fields. The gauge invariance is preserved by extending the Mandelstam path dependent method for electromagnetism. This is done without recourse to Dirac strings or solitons. Further, the energy momentum and angular momentum tensor operators are found explicitly in terms of path dependent variables. A two dimensional charge space is coupled invariantly with the vector boson duet preserving the symmetry of the fermion monopole interactions with the use of the axial vector current, avoiding explicit use of the dual field tensor terms. It is found that if the postulated symmetries are not broken, only part of the Lorentz force law's dual tensor interaction term emerges in the low energy first order in the coupling constant limit. If the mediating scalar field is in the Higg's gauge, the following constraint is found:. 2(pi)n = SQRT.(2m(,0)(lamda)/f, where n = 0, (+OR -)1, (+OR-)2...,. and m(,0) and f are the Higg's model parameters and (lamda) is the coupling constant for the vector boson fields with the scalar fields. The Feynman diagrams are found for the Green's functions in a path dependent, gauge invariant formulation. This situation leads to a specific model for studying the scalar mediating field from a vacuum point of view, and for future work, by breaking the symmetry with the fermion field interaction.
Multi-time wave functions for quantum field theory
Petrat, Sören; Tumulka, Roderich
2014-06-15
Multi-time wave functions such as ϕ(t{sub 1},x{sub 1},…,t{sub N},x{sub N}) have one time variable t{sub j} for each particle. This type of wave function arises as a relativistic generalization of the wave function ψ(t,x{sub 1},…,x{sub N}) of non-relativistic quantum mechanics. We show here how a quantum field theory can be formulated in terms of multi-time wave functions. We mainly consider a particular quantum field theory that features particle creation and annihilation. Starting from the particle–position representation of state vectors in Fock space, we introduce multi-time wave functions with a variable number of time variables, set up multi-time evolution equations, and show that they are consistent. Moreover, we discuss the relation of the multi-time wave function to two other representations, the Tomonaga–Schwinger representation and the Heisenberg picture in terms of operator-valued fields on space–time. In a certain sense and under natural assumptions, we find that all three representations are equivalent; yet, we point out that the multi-time formulation has several technical and conceptual advantages. -- Highlights: •Multi-time wave functions are manifestly Lorentz-covariant objects. •We develop consistent multi-time equations with interaction for quantum field theory. •We discuss in detail a particular model with particle creation and annihilation. •We show how multi-time wave functions are related to the Tomonaga–Schwinger approach. •We show that they have a simple representation in terms of operator valued fields.
ERIC Educational Resources Information Center
Preston, Charles Thomas, Jr.
The work of Paul Hersey and Kenneth Blanchard on life-cycle leadership was compared and contrasted to three studies on group phase theories. The studies on group phases were conducted by Robert Bales and Fred Strodtbeck in 1951, Thomas Scheidel and Laura Crowell in 1964, and B. Aubrey Fisher in 1970. The two theoretical approaches were found to…
Unifying Self-Consistent Field Theory for Weak Polyelectrolytes
NASA Astrophysics Data System (ADS)
Witte, Kevin; Won, You-Yeon
2008-03-01
A self-consistent field (SCF) theory for weak polyelectrolytes has been derived from a grand canonical partition function. The formalism accounts for the location and mixing of the charged and uncharged polymer species, treating the local (spatially dependent) charge fraction as a field variable with which to minimize the total free energy. This method of the derivation gives the resulting equations, especially those governing the local charge fraction, that are identical to the results obtained by Szleifer and coworkers (J. Polym. Sci. B Polym. Phys., 2006) who built upon the mean-field ``annealed'' free energy expression proposed by Raphael and Joanny (Europhys. Lett., 1990). However, we show that these results are further identical to the ``two-state'' model of Borukhov, Andelman and Orland (Eur. Phys. J. B, 1998), namely, the potential field due to the polymer charges with which the chains interact and the local charge fraction are shown to be exactly equal. This annealed model is derived by averaging the partition function with regard to the monomer charges. The charged and uncharged states are weighted by their probabilities which is, in our notation, the bulk charge fraction and one minus the bulk charge fraction, respectively. The utility of this theory is demonstrated by comparing its predictions against various experimental results from bulk potentiometric measurements and also from polyelectrolyte brush compression studies.
How to take particle physics seriously: A further defence of axiomatic quantum field theory
NASA Astrophysics Data System (ADS)
Fraser, Doreen
Further arguments are offered in defence of the position that the variant of quantum field theory (QFT) that should be subject to interpretation and foundational analysis is axiomatic quantum field theory. I argue that the successful application of renormalization group (RG) methods within alternative formulations of QFT illuminates the empirical content of QFT, but not the theoretical content. RG methods corroborate the point of view that QFT is a case of the underdetermination of theory by empirical evidence. I also urge caution in extrapolating interpretive conclusions about QFT from the application of RG methods in other contexts (e.g., condensed matter physics). This paper replies to criticisms advanced by David Wallace, but aims to be self-contained.
Reconstruction in quantum field theory with a fundamental length
Soloviev, M. A.
2010-09-15
In this paper, we establish an analog of Wightman's reconstruction theorem for nonlocal quantum field theory with a fundamental length. In our setting, the Wightman generalized functions are defined on test functions analytic in a complex l-neighborhood of the real space and are localizable at scales large compared to l. The causality condition is formulated as continuity of the field commutator in an appropriate topology associated with the light cone. We prove that the relevant function spaces are nuclear and derive the kernel theorems for the corresponding classes of multilinear functionals, which provides the basis for the reconstruction procedure. Special attention is given to the accurate determination of the domain of the reconstructed quantum fields in the Hilbert space of states. We show that the primitive common invariant domain must be suitably extended to implement the (quasi)localizability and causality conditions.